The carjacking of the city vehicle was reported around 10 a.m. in the area of Folsom and Mabini streets and officers began a pursuit after spotting the vehicle in the area of Kansas and 25th streets, Police Officer Niccole Pacchetti said.
The city vehicle then crashed in the area of 16th Street and Potrero Avenue, causing injuries to the suspect and four other people, Pacchetti said.
Two of the five victims were waiting for the bus. Officials did not say if the person who died was at the bus stop or in another vehicle.
MORE: 3 critically injured after car crash sends vehicle into bus stop in SF's Inner Sunset, police say
The suspect, identified as a man, was detained after the crash and was taken to the hospital.
The crash happened near a Safeway and the glass at the front of the store is shattered.
San Francisco police are investigating what led up to the crash.
Anyone with information about the case is asked to call the Police Department's tip line at (415) 575-4444 or to send a tip by text message to TIP411 with "SFPD" at the start of the message.
Bay City News Service contributed to this article.