The 29-year-old German-Armenian man, who was living in Berlin, has shown "relatively strong" signs of suffering from paranoid schizophrenia, spokesman Sebastian Büchner said, a day after a schoolteacher was killed and 32 other people injured in the incident.
Drugs were found in the suspect's flat, he added.
Further investigations will determine whether mental illness was the cause of the crime, but a political motive is currently being ruled out, Büchner said.
READ ALSO: Teacher dead and school pupil injured in Berlin after car drives into crowd
The suspect is accused of driving into passers-by in a busy shopping district in the German capital, mowing down a group of teenagers and killing their teacher before crashing through a shop window.
The incident happened just across from Breitscheidplatz, where an Islamic State group sympathiser deliberately ploughed a truck into a Christmas market in 2016, killing 12.
In Wednesday's case, the silver Renault Clio with a Berlin licence plate first mounted the sidewalk, hitting the secondary school students on a class trip, before returning to the road and then ramming into the front of a perfume shop.
READ ALSO: Berlin in shock after cars ploughs into pedestrians
A female teacher with the group from a school in Bad Arolsen, a small town in the state of Hesse, was killed and a male teacher was seriously injured.
The car was found to belong to the suspect's sister.
Berlin's interior senator Iris Spranger said the investigation was being conducted by the homicide division.
Germany has seen several deadly car rammings since the deadly 2016 Christmas market assault, with most carried out by people who were found to have psychological issues.
Spranger said on Wednesday said there was no "conclusive evidence of a political act" in Berlin and the attack seemed to have been "committed by someone suffering from psychological problems".
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