"All indications are that they have been shot," Dalarna police spokesperson Sven-Åke Petters told the TT news agency.
"They were both lying in the yard."
A dog was also found shot dead.
Police recovered a hunting rifle on the grounds of the farm near where the bodies were found, which is located outside of Fors, north of Avesta.
So far there are no suspects and no arrests have been made.
The victims also have yet to be identified.
A massive police operation was launched earlier on Tuesday following reports of shots being fired on the farm.
"We went there with all of the squad cars we could manage, as well as ambulances," said Petters.
According to police, it was a neighbour who called police about the shooting shortly before 11am, but it remains unclear what took place on the farm.