Police said the gunman was believed to be among those killed and a search for other possible victims was continuing at the school, located in the city of Orebro. The gunman's motive was not immediately known.
"We know that 10 or so people have been killed here today. The reason that we can't be more exact currently is that the extent of the incident is so large," local police chief Roberto Eid Forest told a news conference.
Forest said police believed the gunman had acted alone and that terrorism was not currently suspected as a motive, though he cautioned that much remained unknown. He said the suspected gunman had not previously been known to police.