The Knicks announced that Rose would be unavailable prior to facing the Hawks. He suffered the injury on Friday night in a win over the Charlotte Hornets.
Rose wore a protective walking boot on his foot in Atlanta to relieve pressure.
Coach Jeff Hornacek said Rose also likely will miss the team's game at the Washington Wizards on Tuesday, and possibly more.
"I don't want to say because you never know with an ankle,'' Hornacek said.
Rose underwent X-rays, which were negative, after suffering the injury with 4:19 remaining in the third quarter of the 110-107 win against the Hornets.
"It feels better every day,'' Rose said Sunday. "You know with knee to ankle and hamstring injuries, I just have to take my time with it and listen to my body and I think that's what I'm doing right now.''
Rose said the ankle "started throbbing right away'' but didn't swell.
Brandon Jennings will start in place of Rose, who has started 43 of the Knicks' 48 games this season. He is averaging 17.9 points -- third on the team -- and 4.4 assists.
Rose missed a game earlier this month to handle a family issue, leaving the team without initial explanation. He will enter free agency this summer.
"I feel great," Rose said. "Playing the amount of games I'm playing in I almost feel like a rookie."
Rose's health was a concern entering his first season with the Knicks. The 2010-11 MVP played a total of 49 games from the 2011-12 season to the 2013-14 season because of injuries. In the previous two seasons, Rose played 51 and 66 games before joining the Knicks.
The Associated Press contributed to this report.