Bo Kellerth of the Jonkoping police said Monday the lock on the minks' cage had been broken, the Swedish news agency TT reported.
"No one has left any message after them nor taken responsibility, so we don't have much to go on," Kellerth said.
Kellerth said there had been demonstrations outside the farm during the summer against mink breeding but said he didn't know if the farm had been subjected to any attacks.
The escaped minks were spotted by a passing motorist as they ran in front of his car Monday.
Kellerth said the owner places a $1.2 million value on the minks.
The newspaper did not make it clear who was under investigation.