The crash happened at around midnight local time (23:00 GMT). The driver, a 58-year-old man, was believed to be the only person injured.
The driver told police he had intended to kill himself, Berlin police said.
Officers found petrol canisters and lighter fluid inside the car, according to local reports.
Investigators were treating the incident as a possible arson attempt and also revealed that the man had earlier left a bag of flammable material in front of the headquarters of Chancellor Angela Merkel’s party, the Christian Democrat CDU, a few minutes’ drive away.
There was no indication that the man, who was slightly injured in the crash, was an extremist, Berlin media said.
It was unclear whether the Social Democrats had been holding a function inside the building, known as the Willy Brandt House, at the time.
Although a fire broke out, the building’s sprinkler system put it out.
The SPD governed in a “grand coalition” with Angela Merkel’s Christian Democrats between 2013 and 2017, but its leaders vowed to end the alliance in September, when the party got its worst results since 1949.
Chancellor Merkel has since been unable to form a majority government with other parties, and the SPD has agreed to “open-ended” talks on a possible new coalition.