It happened at the intersection of Atlantic Boulevard and Hubbard Street. Officials say the driver, believed to be in his 70s, mistook the accelerator for the brake as he pulled into a parking spot.
No customers were in front of the vehicle at the time.
"The ladies inside, they had that look, that smiling look on their face that it was nice that the vehicle stopped short of their counter," said Los Angeles County Fire Chief Thomas Ewald. "Nobody was hurt, nobody was injured. The driver was little shaken up."
The driver suffered minor injuries and was treated at the scene by paramedics.
Fire officials say the structure was not impacted, but personnel from building and safety will check the building to make sure it's safe to occupy.