Santana got hurt on Sunday in Toronto when he collided with teammate Robbie Grossman while trying to make a catch. The team placed him on the disabled list Monday. He was sent back to Minneapolis for tests, which revealed a Grade 2 sprain.
Manager Paul Molitor said before Wednesday's game that Santana will need more than a month to recover, so the team is leaning toward shutting him down for the final month.
A switch-hitter, Santana batting .240 with two homers, 14 RBI and 12 steals this season.