Santana, 35, didn't make his 2018 season debut until late July after having surgery to remove calcium deposits from his right middle finger in early February.
The righty says he hasn't spoken to his surgeon in a while, but "the last time I saw him in New York, he told me the pain will go away. Still here."
Manager Paul Molitor said he's not sure if Santana will return to pitch this season.
"It's a combination of some discomfort and I don't think it's working quite as well. We all see how it's been going to this point," Molitor told reporters, according to the Pioneer Press.
"It's very tough for me and obviously for the team because instead of help the team you hurt the team because you don't locate your fastball where you want it, or your slider where you want it, and then it's difficult," said Santana, who is 0-1 with an 8.03 ERA in five starts. "Now I'm just trying to get ready and move on."
Santana told reporters he's "going to take off to try to make it right, try to make it better, and that way I don't have to worry about it."
Left-handed prospect Stephen Gonsalves will take Santana's spot in the rotation and start Monday's game against the Chicago White Sox. He is 9-3 with a 2.96 ERA in 18 starts for Triple-A Rochester this season.
Santana signed a four-year, $55 million contract with the Twins before the 2015 season. He has a $14 million option for next season that includes a $1 million buyout. He is 30-25 with a 3.68 ERA in 85 starts with the Twins.
In other moves Sunday, the Twins reinstated outfielder Robbie Grossman (hamstring) from the disabled list, recalled Gonsalves and right-hander Alan Busenitz from Rochester and sent outfielder Johnny Field and right-hander Tyler Duffey there in their place.