The incident happened on Friday night as the hunter was chasing boar, the local Tagblatt newspaper reported.
In addition to the four sheep that were killed, three others were injured and had to be put down.
According to the paper, the owner has decided not to take any action after agreeing compensation with the hunter.
The hunter had not been drinking when he mistook the sheep for boar, the paper said, quoting police.
The head of the cantonal inspectorate for hunting and fishing said he had never come across a similar case in 15 years, the paper reported.
He said there were no plans to revoke the man's hunting permit.
Last year a Swiss hunter caused outrage after mistaking donkeys for prey in the Savoie region of France.