The accident happened at around 11:30 am (0930 GMT) at a busy intersection of the western city, and emergency services were quickly deployed to the scene.
Twenty-eight of the injured were taken to hospital, while another 28 were more lightly injured and received treatment at the scene, said a fire service statement.
According to media reports, four people sustained serious injuries, but none were in a life-threatening situation.
The accident appeared to have been caused by one of the trams taking a wrong turn, the Rheinische Post reported. Police have launched an investigation into the incident.
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