Police spokesman Stefan Fardigs said five of the people hit by the bus were seriously injured.
The square was unusually full after the end of the marathon.
Witness Victoria Strand told the daily Aftonbladet that people ran in panic as the bus sped down the steps onto the square.
“Some people didn’t see it and were hit from behind,” she said.
She said the bus also ran over a stroller, but that the child inside escaped without any serious injuries.
Fardigs says the engine raced out of control after the bus started, but it is unclear why that happened.
