The crash happened at around 3.45pm on Nils Ericsons street at the Nordstan tram stop, after one of the trams derailed and crashed into another tram, according to initial police reports.
Some people were taken to hospital, but none with serious injuries.
"Some people are shocked and some have minor injuries, but we're being told from the scene that they have not registered any serious injuries," police spokesperson Ulla Brehm told the TT news agency.
"At the moment I have information about nine people. Two of them have been taken to hospital by ambulance and the other seven are able to seek out a doctor by themselves," she said.
It was not immediately known what caused the tram to derail.
The crash was expected to affect rush-hour traffic in the western Swedish city, which is famous for its iconic trams.
"Traffic has ground to a halt and it will probably take a while to remove the cars," said Brehm at around 4.30pm.
Where the crash happened: