Santana is 0-1 with a 8.03 ERA in five major league starts this season.
"He had one done," Minnesota manager Paul Molitor said Saturday. "I think over a three-week period he'll have that done three times."
Santana had surgery Feb. 6 to remove a calcium deposit on the finger. He made his first minor league injury rehabilitation appearance May 23 and didn't make his season debut for the Twins until July 25.
The two-time All-Star was still bothered by the finger and after five starts returned to the disabled list on Aug. 19.
Santana, 35, is in the final guaranteed season of a $55 million, four-year contract. The Twins have a $14 million option for next year with a $1 million buyout.
"I'm not really sure if the timing of when he picks up a ball will matter nearly as much as his ability to try to get through the winter and put himself in position to pitch again next spring," Molitor said.
Santana is 149-125 with a 4.06 ERA in 14 major league seasons.