Smart appeared to land awkwardly on his right foot at around the 9-minute mark as he was guarding Devin Booker along the baseline. He immediately waved for help after going down and limped off the court with assistance from medical personnel.
Smart had 17 points, three rebounds, four assists, two steals and a block in 30 minutes before exiting.
Smart said he might have tried to return if the game had been close, and there wasn't much swelling after the injury.
"It just irritated the exact same ankle I was coming back from in the same spot,'' Smart said. "But everything's fine. I should be fine to play the rest of the trip.''
Coach Brad Stevens said Smart will be reevaluated on Tuesday.
The Associated Press contributed to this report.