The worst rout in Treasurys since April’s tariff chaos is exacerbating strain in financial markets, a stark demonstration of how war’s disruptions to oil flows are leaving investors with few places to shelter.

The Hormuz blockade has spurred one of the largest oil shocks on record, raising fears of an economic slowdown that have dragged stock indexes to their lowest levels since August. But bonds—often a place of safety in times of market turmoil—have offered no relief, hit by worries that resurgent inflation will keep interest rates higher than expected and undermine the value of their fixed payouts.

The resulting market strain has been painful for both investors and the economy. The iShares Core 60/40 Balanced Allocation ETF, holding a traditional portfolio of 60% stocks and 40% bonds, has lost 6.3% since the fighting started in late February.

At the same time, falling bond prices have driven up the yield on the 10-year Treasury note by almost 0.5 percentage point, lifting borrowing costs throughout the economy. Rates on 30-year mortgages jumped to 6.38% last week, reversing a slide that had carried them to their lowest levels since 2022 and threatening the spring home-buying season.

Some fear the selling has taken on a momentum of its own, with the war-fueled market swings forcing hedge funds to shed bonds to cover bets made with borrowed money and other investors hesitant to step in while the threat of further losses linger.

“Nobody has an appetite to fade this move because if you did try to fade this move in the past couple weeks, it just continues to go against you,” said Izaac Brook, U.S. rates strategist at RBC Capital Markets.

Investors of all stripes were caught off guard by the Iran war, which arrived just as many were growing increasingly bullish on bonds, thanks in part to concerns about potential economic disruptions from artificial intelligence that fueled volatility in the stock market.

On the Friday before the U.S. and Israel first launched a barrage of missiles at Iran, the yield on the 10-year Treasury note had just closed below 4% for the first time since November. Interest-rate futures showed a nearly 80% chance that the Fed would cut rates twice by the end of the year, supporting stocks by offering hope for economic stimulus.

When markets reopened on the Sunday evening after the war started, bonds at first extended their rally in a classic flight-to-safety move—only to reverse course within an hour, as oil prices jumped, raising concerns about inflation.

Many investors still argue that a protracted war could eventually lead to lower yields, by raising energy prices enough to slow U.S. economic growth, creating even more reason for the Fed to cut rates.

At least for now, though, that has been a losing argument. Any sign that the war could continue has sparked a knee-jerk rise in yields, especially for shorter-term Treasurys that are particularly sensitive to shifts in the near-term outlook for interest rates.

Buttressing that trade, Fed officials have at times sounded more concerned about the inflationary impact of the war than its blow to growth. In a postmeeting press conference on March 18, Fed Chair Jerome Powell suggested that officials couldn’t completely ignore an energy supply shock, even if they usually focus on inflation measures that strip out volatile food and energy categories.

As of Friday, the yield on the 2-year U.S. Treasury note was 3.915%, according to Tradeweb, up from 3.377% before the war started. The yield on the 10-year note stood at 4.439%.

Overseas, the threat of higher interest rates is more pronounced. That is in part because the European Central Bank and Bank of England, by statute, are primarily focused on controlling inflation, in contrast to the Fed, which is also tasked with pursuing maximum employment.

Selling in European government bonds has added to the pressure on U.S. Treasurys, given the close links between the two markets, analysts said.

Ritchie Tuazon, a fixed-income portfolio manager at Capital Group, said his team is among those who are bullish on bonds over the long run.

Still, he said, it is much harder to predict what will happen in the near term, with a peace agreement likely leading to a rally in Treasurys and a U.S. ground invasion leading to a further rise in yields.

“Our view is that if there is a ground invasion, that would lead to a weak global growth, which would then be supportive for Treasurys,” he said. “But I think the near-term move would be a selloff.”

Write to Sam Goldfarb at sam.goldfarb@wsj.com