The students were traveling on the truck, being used as a float in a traditional graduation parade.
“Those injured fell off the float. In other words, the truck did not overturn,” said Towe Hägg at Stockholm Police.
Emergency services say seven people are injured. It is not yet clear how badly injured the people are, although at 5.45 pm one had been taken to hospital in Stockholm.
“Many people are in shock,” said police spokesman Gert Andersson.
The accident happened on the bridge crossing Järla station.
The emergency services received the first call about the accident at 5.03pm. Four ambulances were sent to the scene.