The officer, 45, died at the scene. A 44-year-old passenger was seriously wounded, but is expected to survive.
The 41-year-old driver of the tram, which was derailed from the impact, suffered shock, while the few passengers on the tram were unharmed.
The police were responding to a call for emergency backup at about 11:40 pm from fellow officers at a centre for asylum seekers where a violent argument was happening.
The collision with the tram, which was headed in the direction of the city centre, happened moments later at the intersection Moltkestrasse and Erzbergerstrasse.
The police car was hit hard on the left side by the tram, meaning the police driver bore the brunt of the impact. He was trapped in the car and had to be freed by the fire brigade, but paramedics could not save him.
A resident at the asylum seeker centre was injured in an apparent knife attack, police went on to say.
The latest tram accident is the third to transpire in Karlsruhe. Last month, 27 people were injured – six seriously – when two trams collided head on.