Toronto will attempt to give Reyes a start at DH later this week, but there is no immediate timetable for his return to the field.
"They said it's a very mild strain, so hopefully he gets in the next couple days, maybe DH, have him run at half speed, three-quarter speed," Gibbons said. "He's feeling pretty good after getting the results."
Reyes has dealt with this type of injury before. He had two stints on the disabled list and missed 29 games during the 2011 season with a similar injury. Reyes also has missed a handful of games over the years because of hamstring issues, but his only other time on the DL with that injury came in 2004.
The Blue Jays had been saying all week they thought this version of the injury was relatively minor, but it wasn't until the MRI results were revealed that the news became official.
"Yeah, you never really know. ... but he's had a history of problems with his hammies so I'm sure that [tightening] gets his attention," Gibbons said. "We're making sure we'll be good and cautious with it."
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.