The dwindling number of vehicles on dealership lots is threatening to cool the U.S. car market’s blistering sales pace.

Analysts are expecting new-car sales from June to fall off from recent months, when car shoppers turned out in near-record numbers, buoyed by excess household savings and pent-up demand from the pandemic. Most car makers are scheduled Thursday to report U.S. sales results for June.

Customers are still clamoring for a new ride, dealers say. But it has become harder for salespeople to match buyers to vehicles because of the lack of inventory caused by the computer-chip shortage that has hobbled car production since winter.

“We really don’t have enough cars to go around,” said Joe Shaker, owner of Shaker Automotive Group, which sells several brands in Connecticut and Massachusetts. He said his Ford store is carrying about 14% of its normal inventory.

New-vehicle sales in the first half of the year are expected to reach about 8.3 million units, according to an estimate from J.D. Power, a 32% increase over the same period a year earlier and up nearly 1% from the first half of 2019.

But the rate of sales slowed considerably at the end of the second quarter, hovering below an annualized selling pace of 16 million vehicles, J.D. Power estimates. That is down from April, when the industry was on pace to sell nearly 19 million vehicles for the year. The industry tracks the annualized sales rate as a measure of market strength from month to month because it strips out seasonal factors.

Analysts attribute the deceleration to withering dealership inventory. Dealers started June with about 1.5 million vehicles on their lots or en route to stores, down 42% from the same time in 2020 and down 23% from the start of May, according to research firm Wards Intelligence. The diminishing selection is driving prices to record highs.

The average new vehicle sold eclipsed $40,000 for the first time in June, according to an estimate from research firm J.D. Power, with car shoppers routinely paying above the sticker price.

“We’ve been in a full-fledged supply crisis since about June of last year,” said Tyson Jominy, automotive analyst for J.D. Power. “Meanwhile, we have very, very robust demand among some of the wealthiest consumers.”

Consumers are flush with savings from federal stimulus payments and having saved money while hunkering down during the pandemic. Interest rates remain at historically low levels and used-car values have soared, giving consumers higher trade-in values when buying a new vehicle.

The unusual market dynamics—bare dealership lots, eager shoppers and heady pricing—are expected to last at least through the end of the year, analysts and car executives say. Despite the dynamics, many auto makers and dealership groups have reported record profits in recent months, bolstered by the stronger pricing and lower costs.

A Utah Toyota dealership in March. The company has faced supply-chain obstacles.

A Utah Toyota dealership in March. The company has faced supply-chain obstacles.

Photo: Bridget Bennett for The Wall Street Journal

Bob Carter, Toyota Motor Corp.’s North American sales chief, said strong consumer confidence helped the company to its strongest start to the year ever despite having to manage a raft of supply-chain problems.

“We have lots of problems, but I have zero complaints,” he said.

Toyota typically would have roughly 330,000 Toyota and Lexus models on dealer lots in June. It expected dealers to finish the month with around 70,000 vehicles on hand, Mr. Carter said.

Kurt McNeil, General Motors Co.’s vice president of U.S. sales operations, said GM dealers have less than a week’s worth of supply of large sport-utility vehicles, whereas normally they would have enough inventory to last three months.

He said GM expects the semiconductor shortage to ease, but he doesn’t see the situation on dealer lots improving much before the end of the year, and expects inventory to be constrained through 2022.

“There’s so much demand that vehicles are just going to sell” as soon as they hit dealer lots, Mr. McNeil said. “We’re just going to be drastically low for the foreseeable future.”

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Pickup trucks and SUVs, significant profit generators for GM and rivals Ford Motor Co. and Stellantis NV, have been disproportionately hurt by the chip shortage, according to data from research firm LMC Automotive. As a result, the Detroit companies posted falling market shares through the first five months of the year, while rivals Toyota, Honda Motor Co. and Hyundai Motor Co. gained, LMC said.

On Wednesday, Ford said the chip shortage will force it to cut output across more than a half-dozen U.S. factories in July.

Auto makers in general have given priority to the production of their most popular models, while dealers have begun to assign incoming vehicles to customers in an attempt to expedite shipments to their stores.

Higher used-vehicle prices also are helping drive new-car sales, analysts say, because shoppers are eager to leverage the higher value of their trade-ins. Used-vehicle prices on average were up an estimated 36% in mid-June from a year earlier, according to auction firm Manheim Inc.

The hot used-car market and dearth of shipments from the factory have left car dealers scrounging to feed their preowned vehicle lots.

Mr. Shaker said the new-vehicle selling price is no longer his priority in negotiations. Instead, he is telling salespeople to find customers who have a used vehicle they are willing to trade in.

“Right now, it’s far more important for us to sell to someone with a trade-in, because we need more vehicles to sell,” Mr. Shaker said. “When you’re running out of cars, a customer with a trade at least gives you two bites at the apple.”

—Ben Foldy contributed to this article.

Write to Nora Naughton at Nora.Naughton@wsj.com and Mike Colias at Mike.Colias@wsj.com