Cecil posted a 1-2 record with a 6.86 ERA in four outings this season. He allowed 35 baserunners over 21 innings and had yet to pitch more than six innings in any start.
"It's clear that Brett is extremely frustrated," Blue Jays general manager Alex Anthopoulos said. "We just think from a timing standpoint, this is the right move for us and also the right move for Brett.
"This gives him a chance to catch his breath a little bit, get his confidence back. I think everyone has seen that the performance is starting to wear on him, and he wants to do as well as anybody and he hasn't been able to do it."
The 24-year-old has been suffering from a loss of velocity on his fastball. Cecil is used to throwing from 90-94 mph, but during Spring Training and the early stages of the 2011 season, he was consistently clocked in the mid-to-high 80s.
That loss of velocity caused him to overthrow the ball at times in an effort to increase speed. That led to his pitches being elevated in the zone and success for opposing hitters quickly followed. Cecil's opponents batting average is .304, and he has walked 11 batters.
"I think it's more delivery-related than anything else," Anthopoulos said. "Brett, if anything, is a strike-thrower, and the walk totals have started to creep up.
"People have talked about velocity, but it's about command. If Brett's throwing strikes and he gets to his secondary stuff, he's fine. His command hasn't been the same, and I think there are some things with his delivery that he needs to get straightened out.
Cecil led the Blue Jays with 15 wins in 2010 while posting a 4.22 ERA. He entered this season as the club's No. 3 starter, but he will now attempt to improve his mechanics at Triple-A.
"It's a better environment to be able to work on things down there, when the games don't mean as much," Anthopoulos said. "They're not life and death the way they are here. Certainly the impact is not as great."
The Blue Jays must decide who will start Tuesday's game against the Rangers. It appears unlikely that either Marc Rzepczynski or Carlos Villanueva will make a spot start out of the bullpen, which means the candidate is expected to come from the Minor Leagues.
The club could recall left-hander Brad Mills, who has allowed just two earned runs over 22 innings for Las Vegas. Other possibilities include top prospect Zach Stewart or veteran Scott Richmond.
Right-hander Jesse Litsch could be added to that list, but since he was just sent down to Triple-A on Tuesday, he must wait 10 days before being recalled unless a player gets placed on the disabled list.
"We've got some ideas, we just haven't finalized it yet," Anthopoulos said. "Hopefully at some point by the end of the weekend.
"We're going to continue to talk about it -- we've kicked around some ideas, but we haven't named anybody."
The Blue Jays selected the contract of veteran infielder Chris Woodward to fill out the 25-man roster. Woodward has spent 11 seasons in the Major Leagues, and he has hit .241 with 33 home runs and 191 RBIs.