Warning signals are starting to flash in the market for junk debt, an indicator that investors are worried that companies with high debt loads could be at risk even if the U.S. economy avoids recession.

The current change in sentiment is modest compared with the one that hit high-yield bonds in December. But it continued through a recent surge in demand for Treasurys and investment-grade corporate debt. The combined trends expose cracks in the recent rally that has powered the Dow Jones Industrial Average to within 0.6% of...