At the start of 2016, Americans were bracing for interest rates to rise significantly for the first time since the financial crisis.

Instead, rates have slumped anew, rattling financial markets and undoing the plans of investors, consumers and businesses alike.

A little more than a month after the Federal Reserve lifted its benchmark rate from near zero, rates across the market are falling. The yield on the 10-year U.S. Treasury note, a benchmark for everything from mortgage rates to corporate lending, this week fell below 1.7%, its lowest level in a year. On two-year notes, a widely watched gauge of bank funding costs, yields have also dropped significantly.

The slide has alarmed investors because borrowing costs tend to rise in a healthy economy, reflecting growing demand for money among consumers and businesses and bolstering the profits of banks and other financial firms.

Instead, shares across the financial sector are tumbling along with rates. The KBW Nasdaq Index of large U.S. banks is off 18% this year, compared with a 9.4% decline in the S&P 500. The slump reflects expectations that low rates will be with us for years, hurting the profitability of banks and squeezing insurers, asset managers, pension funds and others.

For now, Fed officials are keeping their options open, but the odds of another rate increase this year appear to be getting slimmer. Fed Chairwoman Janet Yellen begins two days of congressional testimony on Wednesday and could clarify the near-term outlook for Fed policy.

The stock-market selloff is the latest sign that many of the gains of low rates have been harvested, while costs continue to pile up, analysts said—particularly for savers who have been struggling with meager interest rates since the financial crisis.

Cathy Berger, a 55-year-old who lives in Nassau County, N.Y., and works as development director at the Queens Chamber of Commerce, said that in the years before the financial crisis she used to invest a large portion of her savings in certificates of deposit, earning an annual rate of as much as 8%.

She moved a portion of her savings into high-dividend stocks after rates fell, but lately those stocks have been under pressure amid turbulence across the financial markets.

“It’s so volatile,” said Ms. Berger. “Trying to reap any kind of income from your money, from your assets, is almost impossible now.”

Many investors and economists see the era of low interest rates continuing for some time. Friday’s jobs report for January confirmed that the U.S. economy, while unspectacular, remains enough of a haven to keep luring capital from sputtering emerging economies. Easing policies followed by developed-country central banks from Japan to Europe are gutting yields there, also helping to drive down rates in the U.S. Yields fall as bond prices rise.

It is possible that the turbulence in financial markets will pass and the economy will continue to grow, produce jobs, push up wages and gradually generate more inflation, which is the Fed’s expectation. If that happens, officials could continue to push rates up.

But a growth slowdown or downward pressure on inflation could convince them to revise their economic projections down and put off additional rate increases.

“Recent developments reinforce the case for watchful waiting,” Fed governor Lael Brainard told The Wall Street Journal this month.

Fed officials penciled in four rate increases in 2016 when they met in December. Traders in futures markets see less than a 50% chance the central bank will even move once before year-end.

Among the biggest casualties of the fall in interest rates have been large U.S. banks. Falling rates squeeze banks because they make money on the spread between the interest charged for loans and payments made to customers on deposits.

Other financial firms have also suffered. Low rates punish institutions such as pension funds and insurers, which hold long-term assets to pay future claims, by making those claims larger in present-value terms than they were when so-called discount rates were higher.

While low interest rates should be a boon to borrowers, there have been indications that lending conditions in some corners of the economy are tightening. Last week, for example, the Fed released a survey of senior loan officers showing that standards on commercial and industrial loans tightened in the fourth quarter and are expected to keep tightening in 2016.

Low-rate stimulus increasingly is “offset by presumably weaker income growth, greater uncertainty and potentially tighter credit conditions,” said Michelle Meyer, a U.S. economist at Bank of America Merrill Lynch.

To be sure, low rates remain a boon for companies like mortgage lenders and auto makers, who sold a record 17.5 million new cars in the U.S. last year.

Jeff Carlson, who owns three dealerships in western Colorado that sell Subaru and Ford vehicles, said two of his stores notched record sales in 2015, which he attributed to the ready availability of cheap financing, as well as low gas prices and a busy ski season in the region.

“Vehicles are as affordable for the consumer as they’ve been in recent memory,” Mr. Carlson said.

Yet many analysts and investors say it’s hard to see auto sales growing at their current clip for much longer, and car maker stocks have suffered this year. Shares of General Motors Co. have fallen 18%, while Ford Motor Co. shares have lost 19% year to date.

“It’s starting to feel like we’re pulling sales ahead,” said Steven Szakaly, chief economist for the National Automobile Dealers Association. “The sales pace is very hard to sustain going outward without some rise in wages and income, or some increase in incentives” from manufacturers.

A similar dynamic has been taking hold in the housing market. For the week ended Thursday, the typical rate on a 30-year fixed-rate mortgage was 3.72%, its lowest since April, according to mortgage-finance company Freddie Mac.

Linda McCoy, a mortgage broker with Mortgage Team 1 Inc. in Mobile, Ala., said persistently low rates have helped encourage some home buying, since borrowers who are also selling a home don’t feel the pain of giving up a low-rate mortgage. But very few simply want a lower rate anymore, she said.

“Most people have already refinanced,” she said.