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In November, nearly 87{e9f0aada585b9d73d0d08d3c277fd760092386ec23cac37d50f4b8cd792b062a} of all new vehicles bought by individual customers sold at or above the sticker price, according to research firm J.D. Power. That number is up from about 75{e9f0aada585b9d73d0d08d3c277fd760092386ec23cac37d50f4b8cd792b062a} at the halfway point of the year, and well above the pre-pandemic average of about 36{e9f0aada585b9d73d0d08d3c277fd760092386ec23cac37d50f4b8cd792b062a} of sales.

The availability of both new and used vehicles is at historic lows, and car companies and dealers are responding by eliminating discounts and adding upcharges to the manufacturer’s suggested retail price, which is the figure displayed on the window sticker when a vehicle leaves the factory. Upcharges include selling items such as tire protection and vehicle accessories.

In addition, dealer markups—which appear as a “market adjustment” affixed next to the window sticker—are also proliferating more broadly. These dealer-price adjustments are separate from upcharges and traditionally have been reserved for rarer models. Now such adjustments appear on everything from no-frills vehicles to new, special-edition SUVs such as the Ford Bronco, dealers and analysts say.

“It’s the basic economics of supply and demand,” said Vince Sheehy, president of Sheehy Auto Stores in the greater Washington, D.C. area. “As long as we have customers waiting for the next car to show up on the lot, there’s no way we can price lower.”

Behind the markups is a historic shortage of new vehicles caused by production lost to Covid-19-related shutdowns and a global computer-chip shortage that has slammed the auto industry this year. At the same time, car buyers have flocked to the showroom in the past year, seeking vehicles for commuting, instead of taking public transportation.

Paul Walser, a Minnesota dealer and chairman of the National Automobile Dealers Association, isn’t charging above sticker for his new cars but says he understands why some smaller dealerships may have to raise their prices. He pointed to dealers he has visited lately who have seen monthly transactions plummet and are looking for ways to cover their business expenses.

“The market is not only changed by the fact that there’s limited supply and high demand,” Mr. Walser said. “Dealers are also sensitive to their costs and making sure that they’re providing for their employees.”

Mr. Sheehy is using markups as a way to filter out one-time customers, he said. When he listed vehicles at or below sticker earlier this year, he said customers drove from hundreds of miles away to buy from him. He said those customers are less likely to come back for service or to purchase another vehicle.

“We really don’t want to sell cars to people who are not going to be our customers in the long-term,” he said. For his most loyal customers, Mr. Sheehy says he is offering to wave the price increases and sell at sticker.

The steady rise in car prices is contributing to an increase in the average price paid for a vehicle, which has hovered around $44,000 for the past two months, according to J.D. Power. That figure is about a $10,000 increase from the average price paid for a new vehicle before the pandemic, the research firm found.

Car shoppers won’t find much relief on the used-car lot, according to dealers and analysts. Prices on preowned cars have been steadily rising in the past year, with some used cars selling at or above their original sticker price. Through the first half of December, the average price paid for a used vehicle surpassed $30,000 for the first time, according to J.D. Power.

This rapid price inflation is also pricing many Americans out of the car market, furthering a trend that has emerged during the pandemic where production of more expensive vehicles is prioritized over cheaper models, according to dealers and analysts.

Some dealers are less willing to charge above sticker. Chris Hemmersmeier, chief executive of Jerry Seiner Dealerships in the Salt Lake City area, is refusing to raise his prices, even as he faces pressure to do so from his sales staff and managers, who say they could be making more money.

Mr. Hemmersmeier, who the second generation to run the family-owned dealership group, said he is worried about the long-term effects of price increases.

“I want this to continue to be a multigenerational family business,” he said. “We can only do that if the community continues to choose to do business with us in good times and bad times.”

The squeeze the parts crisis is putting on vehicle inventories is expected to last until well into 2022, industry executives and analysts say.

There were a little more than a million new vehicles on U.S. dealer lots or in transit at the end of November, down 63{e9f0aada585b9d73d0d08d3c277fd760092386ec23cac37d50f4b8cd792b062a} from the same month in 2020, according to research firm Wards Intelligence.

With supply tight, cars are moving off dealer lots at a blistering pace. More than half of the vehicles sold in the U.S. last month were in the showroom for less than 10 days, according to J.D. Power. The average amount of time a new vehicle sits on dealer lots is hovering around 19 days, J.D. Power found, compared with 48 days at this time last year.

Auto executives are trying to find workarounds to the semiconductor shortage, including dropping some features to save on the number of chips needed to manufacture a vehicle. Some car companies, such as

Ford Motor Co.

and

General Motors Co.

, are taking control of their chip supply by forging partnerships with some of the biggest names in semiconductors.

Even after production normalizes and the automotive industry moves past the chip shortage, J.D. Power automotive analyst Tyson Jominy said the pent-up demand will continue to put pressure on vehicle inventories.

“We expect to see this tightness on inventory lasting clear through 2023,” he said.

Write to Nora Naughton at Nora.Naughton@wsj.com