San Jose fire Capt. Cleo Doss said fire crews were called to Terminal A's Gate 7 at 7:54 a.m.
"Upon arrival the fire was contained to the engine," Doss said. He said it did not spread to the plane's cabin.
Airport spokeswoman Rosemary Barnes said the MD-90 plane, Delta Air Lines Flight No. 1056, had pushed back from the gate at 6:40 a.m. and was scheduled to depart for Minneapolis but was delayed because of fog.
When the pilot later reported a possible engine fire, the plane returned to the gate and passengers were taken off the aircraft, she said. No injuries were reported.
Barnes said the fog was so thick at the airport this morning that planes couldn't take off. She said that as of 7:30 a.m., about a dozen inbound and outbound flights had been delayed.
Travelers are advised to check with their airlines for flight status before heading to the airport.
A Delta Air Lines spokesperson was not immediately available for comment.