Reyes visited a specialist in Charlotte, N.C., on Monday who confirmed the diagnosis of a severely sprained ankle. Reyes was injured when he slid awkwardly into second base in Friday's game at Kansas City.
Anthopoulos said Reyes will be in a cast for two weeks and then in a walking boot for an additional two weeks, meaning he won't be ready to begin rehab activity for at least a month.
Reyes was placed on the 15-day disabled list Saturday. The Blue Jays called up shortstop Munenori Kawasaki from triple-A Buffalo to replace him on the roster.
Reyes was acquired from the Miami Marlins in a 12-player trade last November. The four-time all-star is batting .395 with one homer and five RBIs this season.
Also Monday, Blue Jays slugger Jose Bautista was not in the starting lineup for the opener of a four-game series against the visiting Chicago White Sox.
Bautista is fighting a cold and is resting a sore back. Anthopoulos said the veteran right-fielder will likely return to the lineup Tuesday night.
The Blue Jays are in the middle of a 20-day stretch without an off day.
Bautista missed a few games earlier this month with an ankle injury. He has three homers and six RBIs in nine games this year.
With files from The Associated Press.