The 30-year-old began a rehab assignment on July 13 and the Blue Jays are expected to use the entire 30 days before he has to be removed from the disabled list.
"Happ was just OK in his last [start] so I don't know what his time frame is, but he's not too far away, probably a couple of more starts," Blue Jays manager John Gibbons said. "One or two at the most I would think barring any setbacks."
Happ surrendered six runs on eight hits over 4 2/3 innings during his last outing for Triple-A Buffalo. He has allowed seven runs in two starts for the Bisons and previously made an appearance for Bluefield and Class-A Dunedin.
Gibbons also said that he doesn't expect either Drew Hutchison and Kyle Drabek to return before September. Both right-handers underwent Tommy John surgery last season and are currently pitching in the Minor Leagues.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.