The gun was discovered Saturday in the town of Umea, the Swedish news agency TT reported.
The children apparently thought the gun was a toy and fired it at the ground, TT said.
"It [the gun] made a loud bang and they ran off to an adult who called us. He then looked after the weapon until a police patrol arrived," said Simon Wormo of the Vasterbotten police.
When police arrived, they discovered the gun had another live bullet in its magazine.
"It could have gone really badly. The children could just as well have started playing a war game and begun shooting at each other. It is also an area with lots of people and children milling about," Wormo said.
Police are running a background check on the gun to try and find its owner.
"We are trying to establish if it is a legal weapon, if it has been reported stolen or has been used in a crime," Wormo said.