Firefighters had to use the Jaws of Life to free the passenger in a minivan involved with Brady's Audi in the Thursday morning accident, the Boston Herald reported.
The man extricated from the van was conscious by the time he was taken into the ambulance, witnesses said.
Brady refused treatment at the scene and was reportedly on his way to Gillette Stadium for practice, a team source said.
Emergency Medical Services personnel transported one person to a hospital, spokeswoman Jennifer Mehigan said.
A witness said Brady was driving south on Commonwealth Avenue in the Back Bay area of Boston and had a green light when the minivan went through a red light and the two cars collided, The Boston Globe reported.
The Patriots are preparing for their season opener Sunday against the Cincinnati Bengals.
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