KAMPALA, Uganda—Ten million people face hunger in the Democratic Republic of Congo’s east, and it isn’t because there is no food to be had. It is largely because people can’t get what food there is.

The M23 rebel group that one year ago seized Goma, eastern Congo’s largest city, has tried to establish itself as the prevailing government in the area and consolidate control. Instead, it has driven farmers from their land, left produce to rot at roadblocks and blocked food imports except those from its allies in neighboring Rwanda, according to local traders and activists.

The result is empty shelves in most stores and sky-high prices for meat, milk, grain and vegetables in stores that do manage to stock up, residents and activists report.

Noella Amisi, a nurse in Goma, rushed out for baby formula, sugar and other groceries as soon as she received a $30 mobile-money transfer from her husband in government-held Kinshasa, Congo’s capital city. For hours, she crisscrossed the city looking for a stocked supermarket. She found nothing to buy.

“I am just trying my best to ensure that my children don’t starve, but every day the situation gets worse,” said 28-year-old Amisi.

The United Nations projects three million people in eastern Congo will likely slip into a food emergency by the end of June—its term for life-threatening hunger.

After years of insurgencies, residents in eastern Congo are accustomed to food shortages, inflation and destitution. But since the Rwandan-backed M23 stormed through the mineral-rich region and seized Goma and Bukavu, the region’s No. 2 city, people have had to comb looted markets for scraps of food. Some locals sell clothes and other personal items to raise cash to buy what high-priced food they can find.

Across rebel-held cities and towns, supermarket shelves sit empty while crops wither in inaccessible fields and go bad at rebel checkpoints.

Rwanda’s quest to solidify its influence in eastern Congo has prompted it to deploy its military, which fought alongside the rebels and is now helping M23 create what is de facto an autonomous region in the country’s mining heartlands, according to U.N. investigators.

Rwanda’s economy has become one of Africa’s fastest-growing, thanks in part to smuggled Congolese minerals, according to economists.

But by choking off agricultural production, transport and markets, Rwanda’s M23 allies are aggravating Congo’s hunger crisis. Analysts say Congo’s situation is reminiscent of the insurgency that created the 1985 famine in Ethiopia, which killed nearly one million people, and the continuing conflict in Sudan, which has turned the country’s breadbaskets into hunger spots.

“The M23 rebel group is inflicting deeper suffering on civilians through brutal tax collection and tight controls over food trade and property ownership,” said Richard Moncrieff, an analyst with the International Crisis Group.

Rebels block dairy and beef from entering Congo—except if it comes from Rwanda, traders and residents say. In some areas they control, rebels allow merchants to import cooking oil, rice and wheat from other neighboring countries only if cleared by the Rwandans, residents and traders say.

For several weeks, a supermarket owner in Goma hasn’t been able to restock the cold-storage section, where he normally keeps perishables. The trader said he lost $60,000 last month after a container he imported from Kenya was impounded at the Congolese border for several weeks, rendering milk, cheese and sausages inedible.

“Eastern DRC has long been a covert economic engine for Rwanda through its illicit networks and proxies,” said Zobel Behalal, senior expert at the Global Initiative Against Transnational Organized Crime, a Washington-based think tank. “M23 now functions as the armed extension of Rwanda’s influence.”

M23 and the Rwandan government didn’t respond to requests for comment.

Early last month, Amisi, a mother of three, sold most of her clothes, her television and other personal belongings, but could still only afford a 66-pound bag of corn flour, enough to feed her family porridge once a day for three weeks. She couldn’t raise enough to buy a 44-pound bucket of rice. The price for rice had doubled—to the equivalent of $25—in just a few days at stores that had any to sell.

Since then, stocks have largely dried up. “Most of the shops and supermarkets are closed,” she said. “The few that are open don’t have supplies. I just returned home with nothing.”

President Trump says he ended the war last year with a Congo-Rwanda peace agreement. The rebels, however, weren’t part of that accord, and so violence continues. The war has uprooted more than three million people across Congo over the past year.

After rebels seized the region, Congo’s central bank suspended banking there. The government used to collect up to $900 million in taxes each year, according to government data.

M23 has struggled to obtain fuel and food for its own fighters because the rebels can’t extract taxes from residents who can’t access cash.

To plug the shortfall, M23 relies on Rwanda for operational funding, according to U.N. investigators. In exchange, Rwandan products are granted a monopoly in markets in rebel-held areas.

Rwanda denies supporting M23 and says its troops are in eastern Congo for “defensive measures” against a rebel group formed by Hutu extremists who orchestrated the 1994 genocide in Rwanda before fleeing to Congo.

Patrick Muyaya, Congo’s communications minister, says Rwanda is intentionally squeezing the Congolese people by restricting aid and food flows.

“This campaign cannot be justified as self-defense,” Muyaya said in an interview. “It is an effort to secure economic control through a proxy armed group.”

A few miles north of Goma, M23 rebels allegedly killed 300 farmers last year, leading to an exodus from key potato- and vegetable-growing lands, according to U.N. investigators. Most victims were camping in their fields during planting season when M23 targeted people they suspected of supporting pro-government militias, torching homes, the investigators reported.

Some 70,000 residents from Rutshuru District fled to Uganda because of the September attack, according to the U.N.

“Insecurity has resulted in the loss of access to productive land and local food production,” said Patrick Andrey, Congo country director at Action Against Hunger, a New York-based charity. “The high risk of violence makes it extremely challenging for humanitarian workers to reach people who need support.”

M23 rebels have since taken over farmlands and prevented locals from harvesting any crops, according to Twizere Sebashitsi, who heads a Congolese activist group, Rutshuru Territory Youth Council.

Sebashitsi recalls how his 25-year-old neighbor, Samuel Mukanda, defied a rebel order to vacate his 5-acre potato and cassava farm. Mukanda, whose wife had given birth weeks earlier, ignored the rebel ultimatum and instead tried to harvest his crops. When the rebels returned the following day, they beat him and three other workers, Sebashitsi said. Mukanda lost his front teeth.

“They are not allowing anyone into the gardens,” Sebashitsi said. “Farmers who dare defy them sometimes get killed.”

Many Goma residents previously relied on relief supplies delivered through the city’s international airport, but the rebels have shut the airport down, hobbling aid groups’ efforts to replenish depleted stocks.

The U.N. says it urgently needs $350 million to keep aid efforts running in Congo over the next six months but has so far raised less than 20% of the required funds.

Write to Nicholas Bariyo at nicholas.bariyo@wsj.com