Reyes visited a specialist in Charlotte on Monday who confirmed the diagnosis of a severely sprained ankle. Reyes was injured sliding into second base in Friday's game at Kansas City. He was placed on the 15-day disabled list Saturday.
Anthopoulos says 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.
Acquired from Miami in a 12-player trade last November, the four-time All-Star is batting .395 with one homer and five RBIs.
Blue Jays slugger Jose Bautista was held out of the starting lineup for Monday's game against the White Sox because of a sore back. Normally an outfielder, Bautista has been playing third base since Reyes was injured, but is expected to return to right field when he plays again.
Also Monday, the Blue Jays promoted right-hander Ramon Ortiz from Triple-A Buffalo and designated outfielder Casper Wells for assignment.
An 11-year veteran, Ortiz has a career record of 86-84 and ERA of 4.93 in 296 games with seven teams.