An MRI on Tuesday confirmed the injury after he was held out of Monday night's game against the Orlando Magic.
The team also confirmed that he'll be reevaluated daily after first experiencing discomfort following Cleveland's 96-91 win against Atlanta on Saturday.
Garland is Cleveland's second-leading scorer at 17.2 points per game and the team leader in assists (6.3) in his second season. Injuries have mounted in Cleveland after the team started 3-0 for the second time in the past 20 seasons and the first without LeBron James on the roster since 2000-01.
Dante Exum is also expected to miss 6-8 weeks with a right calf strain, Tuesday's MRI revealed. Exum's injury happened in the opening quarter of Monday's game in Orlando.
Kevin Love aggravated a right calf strain that was initially diagnosed during the preseason during a Dec. 27 home win versus Philadelphia and was set to miss 3-4 weeks. Cleveland is currently 4-3 overall.