The Twins announced the move on Wednesday. The 29-year-old Wilk was the Mets' emergency starter on Sunday when Matt Harvey was suspended. He started six games for Triple-A Las Vegas this season, going 2/3 with a 5.91 ERA.
Minnesota has been in the middle of a shuffle of the starting rotation after sending Kyle Gibson down to Triple-A Rochester last week. The Twins currently have an opening in the rotation for the game Saturday at Cleveland and Wilk could slide into that spot.
Wilk will join the Twins on Thursday in Chicago, where they are playing the White Sox.