The pair were looking to park near Basel SBB train station at around 8.30am on Wednesday morning when the 72-year-old female passenger told the 77-year-old driver to turn right into what she thought was the entrance to the car park, Basel police said.
Instead it was a flight of steps down to the station's post office.
The car had already started rolling down the steps when the driver realized his mistake.
The pair were unharmed and no one else was hurt in the incident, however there was some damage to the steps and the car had to be removed, police said.
The driver risks being charged with driving without due care and attention.