The last time mortgage rates were this high, the dot-com bubble had recently burst. Rates were on the way down. They were in the middle of a four-decade stretch in which they mostly fell, underpinning the growth of the modern mortgage market and boosting the rate of homeownership.

Interest rates reversed sharply this year, pushed up by the Federal Reserve’s aggressive rate increases meant to curb inflation. The monthly cost of borrowing to buy a home has surged because of the additional interest buyers must pay at higher rates. That is on top of a pandemic housing boom that pushed prices up sharply.

A buyer who puts 20% down on a median-priced home would have a monthly payment of $2,259, according to listings website Realtor.com. That is up 75% from a year ago, when the monthly payment was $1,296. (Realtor.com is operated by Wall Street Journal parent company

News Corp.

)

That has tripped up would-be buyers like Pat Nerney and Kait Hardiman. Since the spring, they have been looking for a bigger home in Tampa, Fla., to prepare for the birth of their second child. The rise in rates has reduced the amount they can offer on the new house by more than $100,000, Mr. Nerney said. They haven’t been able to find a house that meets both their criteria and budget.

Mr. Nerney said they have made multiple offers at below asking price, but haven’t gotten sellers to cut prices by more than a few thousand dollars. The deals fell through.

“The seller is stuck on a price,” he said. “The people trying to buy are stuck with whatever their budget is.”

The housing market is at the center of the Fed’s efforts to curb inflation by jacking up interest rates. Home prices rose quickly last year and helped drive up overall inflation. But higher rates have pushed potential buyers out of the market.

In September, existing-home sales fell 24% from a year earlier, and new-home sales were down 18%. Home prices are starting to slip month-over-month, though it does little to offset the increased costs of buying. Prices are still rising compared with a year ago.

By one measure, the rise in rates over the past several weeks has been the fastest on a percentage basis in records going back half a century. That speed has been particularly destabilizing, mortgage lenders and real-estate agents say.

“Everyone is like, ‘I don’t know what to do so I’m just not going to do anything,’” said Ralph DiBugnara, senior vice president at residential lender Cardinal Financial, who is based in New York City. “People are just fearful.”

Sales are still happening, albeit at a slower pace. Some who have waded in say they prefer the calmer clip of this year’s market compared with last year’s, when homes were selling sight-unseen and bidding wars were common.

“The volume has definitely slowed but people are definitely still looking for homes,” said John Hastings, senior loan officer at Intercap Lending in Colorado Springs, Colo. He said that roughly a third of his prospective clients had decided to wait out the rise in mortgage rates.

Buyers who do move ahead with purchases are turning to adjustable-rate loans in greater numbers. Others are using loans that lower the rate for the first couple of years.

But the drop-off in buyers has taken the steam out of what was a hot market.

John Hussey started thinking about selling his home in Massachusetts in April, but by the time he got some repairs done and got it on the market in June, rates were higher and the market had cooled.

His real-estate agent recommended he sell it for $30,000 less than they discussed previously. He thought there might be a bidding war due to the lower price, but he ended up getting one offer at asking price. He accepted.

He closed in September and moved to be closer to family in the Chicago area. “There’s a lot of built-in stress,” he said.

Since then, the market has continued to slow down.

“All of my listings right now are just sitting on the market,” said Alison Williams, a

Redfin Corp.

real-estate agent in the Sacramento, Calif., area. “They are well over 30 days on the market. Six months ago, four days on the market would have been a long time.”

Write to Ben Eisen at ben.eisen@wsj.com