American utilities are facing the highest natural-gas prices in years as they build stockpiles for winter. The reason: Exporters are sending more gas than ever to countries starved for the fuel.

Pipelines to Mexico and Canada and tankers traveling to Europe and Asia have moved record amounts of U.S. gas out of the country this year as parts of the world fall short of supplies. American frackers, meanwhile, are holding the line on new drilling as investors pressure them to maintain capital discipline and return money to shareholders.

The result is that natural-gas exports are pushing domestic prices higher—only the second time this has happened since companies began shipping shale gas from the Gulf Coast to other countries in 2016, other than a brief period during the February freeze in Texas, analysts say.

U.S. Henry Hub gas prices closed Friday at $5.516 per million British thermal units. That is up from just over $3 per million British thermal units a year ago.

The pinch shows a growing tension between exporters and buyers who have enjoyed cheap gas for more than a decade. Some manufacturing and chemical companies have built entire businesses around low U.S. gas prices.

Utilities from the Pacific Northwest to New England have filed regulatory requests to raise rates for natural gas this winter, citing a supply squeeze as a result of higher global demand. The Energy Information Administration has forecast that the average U.S. household that relies on natural gas for heating will pay 30% more for the fuel this year.

Eversource Energy, a utility that serves 3.6 million electric and natural-gas customers in Connecticut, Massachusetts and New Hampshire, warned this month that average natural-gas customers in Connecticut can expect to see their bills increase by about 14% this month. In Massachusetts, customers may see bills increase by as much as 21%.

James Daly, Eversource’s vice president of energy supply, said the company typically stores enough gas to meet about a third of its winter needs and relies on the market for the remainder. He said the cost of natural gas has increased by about 20% compared with a year ago, when prices were at historic lows. That has also affected wholesale electricity prices, which are up about 50% in the New England market, Mr. Daly said.

“Demand for natural gas and power is increasing substantially over where it was a year ago,” he said. “We’re seeing a bit of upward pressure on natural gas prices here to respond to the very high demand and the prices in Europe.”

CMS Energy Corp. , a utility serving 6.7 million people in Michigan, is largely insulated from winter price swings because it already has enough gas parked in storage fields. But the surge in exports has made the procurement process more difficult this year, as utilities across the country grapple with short supplies, said Greg Salisbury, the company’s vice president of gas supply and engineering. Already, his team is thinking about next year’s procurement strategy.