The Rockies said Monday the operation will be performed by Dr. Robert Thompson at Barnes Jewish Hospital in St. Louis.
The 31-year-old Wells had a blocked artery in his right arm in 2006, which had to be replaced by a vein taken from Wells' leg. That surgery also was performed by Thompson.
"They're going to take a look at where the clots are coming from," Rockies trainer Keith Dugger said. "More than likely, the clots are coming from the shoulder."
Wells was placed on the 15-day disabled list retroactive to April 29. He was 1-1 with a 2.29 ERA in 10 games, including one start.
No date has been set for his return.
"This isn't about Kip getting well to pitch, this is about Kip getting well," Rockies manager Clint Hurdle said Monday.
Hurdle said Wells and his wife, Emily, are dealing with medical issues concerning their baby as well, but wouldn't elaborate.
"Their baby just had a situation they had to deal with, with a surgery, and now Kip," Hurdle said.
Rockies pitcher Aaron Cook underwent surgery in 2004 for blood clots.