The Celtics announced Smart underwent successful surgery on his thumb and that his timeline to return to basketball activities is six to eight weeks.
After suffering the injury, Smart told ESPN.com's Chris Forsberg it was "sore, but it will be all right. It's like a sprain right now."
The 24-year-old missed Wednesday's overtime loss to the Washington Wizards with the injury and had just returned for eight contests after missing the previous 11 games due to a right-hand injury suffered after punching a picture frame.
In 54 games this season, 11 of which were starts, Smart averaged 10.2 points, 4.8 assists, 3.5 rebounds and 1.3 steals.
He shot 36.7 percent from the field and 30.1 percent from three-point range.
Although Smart is behind Kyrie Irving and Jaylen Brown on the backcourt depth chart, he is a key contributor due to his top-flight perimeter defense.
Boston is second in the Eastern Conference at 46-22 and trails the first-place Toronto Raptors by five games.
Until Smart is able to return, Terry Rozier, Shane Larkin and Abdel Nader will be the primary depth options at guard.