The Blue Jays selected the contract of right-hander Edgar Gonzalez to replace Happ on the 25-man roster, but the club likely will make another roster move this weekend.
"We're worrying about tonight's game," Toronto manager John Gibbons said when asked who would make Happ's scheduled start on Sunday. "When it gets a little closer to that day, we'll let you know."
Veteran right-hander Claudio Vargas could be one candidate to make a spot start as the club waits to see how long No. 4 starter Josh Johnson will be on the disabled list with soreness in his right triceps muscle.
Vargas was scheduled to pitch for Triple-A Buffalo on Wednesday night, but if his outing is relatively short, he could come back on three days' rest to face Boston on Sunday afternoon.
Double-A New Hampshire right-hander Chad Jenkins would be a stronger candidate to make the outing, but he just recently returned from a right shoulder injury. Jenkins made his first start of the season on Monday and allowed three hits and two runs in five innings as he continues to build up endurance.
Jenkins appeared in 13 games -- including one start -- for the Blue Jays last season and posted a 4.50 ERA in 32 innings. The 25-year-old was a first-round pick in the 2009 First-Year Player Draft.
The Blue Jays have off-days next Monday and Thursday, so it's possible the club won't need a fifth starter after Sunday until May 21.
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.