The elder Brady had just arrived in Boston from the family's California home and found out about the accident as soon as he got off his flight.
"Not the way you like to get off a plane," he said.
The team confirmed the accident on Twitter and Facebook.
A passenger in the other vehicle had to be freed with the Jaws of Life and was taken to Brigham & Women's Hospital with serious injuries that are not considered life threatening, Boston Fire Department spokesman Steve MacDonald said.
Police responded to the intersection of Commonwealth Avenue and Gloucester Street at about 6:30 a.m. to reports of an accident between an Audi sedan and a minivan, police spokeswoman Elaine Driscoll said. The intersection is three blocks from Brady's home.
The accident, which knocked over a light pole, remains under investigation.
Bill Barron said he was in his apartment overlooking the intersection when he heard a collision that sounded like "a bolt of lightning."
When he looked out the window, he saw the driver of the car picking glass off his clothes and wiping himself off with a towel. He didn't realize until later that it was Brady.
"I thought it was some college kid who had crashed up his father's really nice car," Barron said.
Brady then retrieved some items from his car, made a series of phone calls and was picked up by another vehicle, Barron said. The Patriots open their season at home Sunday against the Cincinnati Bengals.
Brady has made news in the last couple of weeks because of reports that he is close to signing a major contract extension.