The perpetrator, described as a young man, is dead, a police spokesman told CNN.
Police said the lone gunman began shooting while a lecture was taking place, before running outside.
A police spokesperson told Reuters they believe he killed himself.
One of those shot in the incident was seriously injured, according to CNN’s German affiliate n-tv.
At this stage, officers cannot determine a motive for the incident in the Neuenheimer Feld area of the city, the police spokesman told CNN.
A large-scale police operation is underway: “Police and emergency services are on the scene,” Mannheim Police said in a tweet.