Collins was injured during Tuesday night's loss at Phoenix. He underwent an MRI that showed a lateral ankle sprain and associated bone bruise.
Collins has started low-level rehabilitation activities and will be reviewed in a week, ruling him out for at least five games. The team had two more games on its longest road trip of the season before a four-game homestand.
The Hawks have dealt with a rash of injuries that have sidelined key players such as De'Andre Hunter, Bogdan Bogdanovich and Cam Reddish for significant periods.
Now it's the 6-foot-9 Collins, who is averaging 18.2 points and 7.8 rebounds per game while shooting 38% from 3-point range.
Reddish hasn't played since Feb. 21 because of right Achilles soreness. While he has increased his lower limb weight room work and intends to add limited low-level impact work, the team said he is at least two weeks away from returning.
The Hawks were playing at San Antonio on Thursday night.