The National Highway Traffic Safety Administration said Wednesday its preliminary investigation will involve about 75,000 of the passenger cars from the 2004-2005 model years.
Toyota Motor Sales USA Inc. said in a statement it was "an early-stage inquiry to determine if further analysis is warranted, not a recall."
The company said it was cooperating with NHTSA and would provide the agency with complete results of its own internal investigation. NHTSA investigations sometimes lead to vehicle recalls.
The Prius has been hugely popular in the United States. Some consumers wait months to buy the vehicle, which has a base sticker price of about $21,000. Automotive experts have said it represents the first economy car with a higher resale value.
Hybrid vehicles deliver better mileage and less pollution by switching between a gasoline engine and an electric motor. The vehicles have become increasingly popular with the rise of gas prices.
NHTSA said it has received 33 complaints alleging engine stalling. The majority of the complaints involved reports of the engine stalling at speeds of 35 mph and 65 mph.
Some complaints indicated the vehicle was in electric mode for some period after the gas engine stalled, NHTSA said.
All the reports said the engine shut down without warning. About half said the vehicle wouldn't restart and required a tow after the engine shut off.
One driver said, "I do not have the same confidence in the car...." Another Prius owner wrote, "I was extremely concerned for my safety and would be scared to drive the car again," reports CBS News Correspondent Bob Orr.
Toyota executives noted there have been no reported cases of deaths or injuries from the engine problems.
The Prius has won accolades throughout the industry. Motor Trend magazine named it the 2004 car of the year, and J.D. Power and Associates recently named it the top performer among compact cars.
Underscoring the vehicle's popularity, Toyota reported Wednesday that the Prius had its best-ever May, selling 9,461 of the sedans, up from 3,962 a year ago.
Toyota has sold 43,686 Priuses this year, up from 17,564 sedans sold during the same period a year ago. The automaker has said it plans to double to 100,000 the number of Prius cars for the North American market this year.
Auto analyst John McElroy said the investigation could threaten hybrid sales.
"Look, there's no question that this is very serious for Toyota," he said. "The company has bet the farm on hybrid technology. If it turns out to be a very widespread problem they're going to be in trouble. Then a lot of people are going to say 'wait a minute' -- I'll let them work out the bugs before I go buy this new technology."