Delabar has experienced lingering discomfort for the past several weeks and it finally reached the point where the Blue Jays wanted to play it safe and shut him down for a brief period of time.
"The way [Delabar's latest discomfort] was related to me was that if this was the playoffs, he could pitch, but it's one of those things that it's better to get on top of it right now because it's taking him a little bit longer to get loose and there is inflammation in the shoulder," Blue Jays general manager Alex Anthopoulos said.
"He was examined by the Angels' team doctor here, and they don't think it's anything significant. He's heading to Florida and will be re-examined by our doctors. It looks like he just needs to rest, more than anything else."
Delabar has become one of the most reliable setup men in the Major Leagues this season. He was voted into the All-Star Game last month and is 5-2 with a 2.90 ERA in 49 2/3 innings.
The second-year pitcher also leads American League relievers with 75 strikeouts. There were signs of trouble during his last outing on Friday night when he had a rare off night on the mound, surrendering three extra-base hits en route to taking the loss against Los Angeles.
Happ will make Wednesday's start against the Mariners, matching up with No. 1 starter Felix Hernandez. Happ has been out since early May after being struck on the head by a line drive off the bat of Tampa Bay's Desmond Jennings.
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.