It is believed the attackers specifically sought out the car, which was parked in the western Berlin suburb of Charlottenburg, for the attack which happened last Friday night.
Officially, police would confirm only that they were investigating a case of willful damage but not that the car belonged to Westerwelle.
But an investigator told the paper: “It would have to be a big coincidence if right at the time of the discussion of the German military deployment, an attack on the car of the new foreign minister wasn't deliberate.”
The attack comes at a time of rising concern over political targeting of politicians and other authority figures. At the beginning of this month, part of the Chancellery building, where Chancellor Angela Merkel has her offices, was attacked with light bulbs full of paint.
Other attackers, assumed to be left-wing extremists, threw Molotov cocktails, paint bombs and cobblestones at Berlin's Treptow district Federal Criminal Police (BKA) office. And local offices for the centre-left Social Democrats and the conservative Christian Democrats were also vandalised with anti-war graffiti.