The Erasmus Bridge is a major landmark in the Dutch port city, spanning the Maas river, and a major transport hub.
Webcam footage of the bridge showed a tram steaming into the back of another, sending debris flying across the lanes of traffic and damaging both trams.
The bridge has been closed to all traffic in both directions.
Images show scores of emergency services personnel evacuating the injured with stretchers and wheelchairs.
Rotterdam authorities initially gave a toll of 18 injured, but revised this down to 15, according to national broadcaster NOS.
