The wing of an American Airlines plane clipped the tail of a Southwest Airlines plane, while both were on the taxiway. It happened on Wednesday at 06:05 local time (11:05 GMT) at Detroit Metro airport.
Passengers had to remain on board the planes but there are no reports of any injuries or fuel leaks.
The Federal Aviation Authority has said it will investigate the incident.
Passenger Fletcher Sharpe spoke to the BBC from the airport where he will have to wait until the afternoon for another flight.
He said other passengers commented that the planes were close to each other, but he did not believe they would hit each other until the moment of impact.
"All of a sudden we heard a loud crunch and a scraping sound," he said. "I thought we had run over something. I looked up and the right wing had lost a few pieces and the back tail of the other plane was smashed off.
"It was frustrating. I understand that that's a high stress job. Everyone's depending on you and you have a lot of things on your mind. But it just seems like 101 to make sure you have enough room. You learn that in a car, or when you're walking.
"We just happy we weren't in the air."
Another passenger, Jim Bishop, told Fox 2 News Detroit that he had been kept on board for two and a half hours and information was sparse at first.
He said: "It was ten minutes of silence. Nobody said anything.
"Finally it came over the radio that there had been an accident and to stay calm. A steward walked past and I asked him - he said he'd been in the job for 35 years and this had never happened before. He didn't know what to do."
The temperature was below freezing and the Southwest plane was being de-iced when the accident happened.
Both planes were Boeing 737s.
Southwest Airlines said the plane that had been hit would now be out of service for maintenance. It had been due to fly to Dallas, the airliner said, and 95 passengers would be moved to other flights.
In a statement, the airline said: "We appreciate the patience of our customers as we work diligently to get them safely to their final destinations."
American Airlines apologised to customers for the inconvenience and said the 150 passengers who were on board - also due to fly to Dallas - were being put on other flights.
Two planes have collided on the ground at an airport in Detroit.