Michael Dwyer/Associated Press
Wojnarowski added that Smart will undergo thumb surgery on Friday.
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 game with the injury and had just returned for eight contests after missing the previous 11 games due to a right-hand injury suffered while punching a picture frame.
In 54 games this season, primarily off the bench, Smart is averaging 10.2 points, 4.8 assists, 3.5 rebounds and 1.3 steals.
He is also shooting 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 for Boston due to his top-flight perimeter defense.
Boston is second in the Eastern Conference at 46-22, and it 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.