They then said rules stipulate that planes cannot take off if a mouse is found on board.
The passenger, called Carly, said: "I'm not sure people knew how to react. There was general disbelief."
Some passengers tweeted about the flight, with one writing a Haiku about the mouse.
Another flight was provided for the passengers four hours later.
British Airways said: "We know almost everyone wants to fly with us to San Francisco, but on this occasion there was one very small customer who we had to send back to the gate.
"Everyone with two legs is now on their way to California, and we are sorry for the delay."