The Celtics also lost backup center Daniel Theis to season-ending surgery to fix a torn meniscus.
Shams Charania of Yahoo Sports reported that Smart had a torn tendon in his right thumb, while former colleague and current ESPN reporter Adrian Wojnarowski indicated that the team was calling it a "sprain" and was now in the process of obtaining a second opinion and deciding whether Smart might be able to play through the pain.
Smart will head to the Big Apple to have another examination done on his right thumb, according to NBA.com's David Aldridge. He is expected to receive a second opinion on the thumb, which he injured diving for a loose ball in Sunday's loss to the Indiana Pacers.More news: Shoe memorial represents thousands of victims of USA gun violence
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To make matters worse, the Celtics have listed Al Horford as questionable for their tilt against the Wizards.
Irving will likely have to deal with the lingering soreness for the rest of the season, making Smart's absence that much more painful, with the only healthy bodies of Terry Rozier and Shane Larkin available to play the point guard position.
Smart is averaging 10.2 points, 4.8 assists and 3.5 rebounds per game.