Happ was placed on the 15-day disabled list the following day with a sore back. He threw a bullpen session on April 2 and is now in the process of building up his endurance.
"He threw 70-something [pitches] his last spring game," Anthopoulos said. "He's been shut down for a little bit, so that would be the cap. Somewhere in the 70s, because that's where he's built up to."
Happ dealt with tightness in his lower back for most of Spring Training but still made four starts. He struggled, going 0-2 and allowing 16 earned runs over seven innings.
It is unclear as to where Happ, 31, fits on the Blue Jays' roster when he does return. He could find himself in the bullpen, though an injury to a starter could eventually land him a place in the rotation.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. Jamie Ross is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.