The surgery will be performed Aug. 19 by Dr. James Andrews, the team said in a release Tuesday.
Wagner, 30, is on the Blue Jays' 40-man roster. He split time between Toronto and Triple-A Buffalo this season prior to being placed on the disabled list.
The Minneapolis native had an 8.10 ERA in 10 appearances with the Blue Jays this season and had four saves and a 4.00 ERA in nine games with the Bisons.
Wagner is 2-4 with a 4.92 ERA over 52 major-league appearances for the Blue Jays and Oakland Athletics.