Initial X-rays taken at the arena were inconclusive, according to the Cavs. Smith will travel back to Cleveland with the team and be re-evaluated Wednesday before the Cavs host the Bucks on the second night of a back-to-back.
Smith, who signed a four-year, $57 million extension with Cleveland in the offseason after the Cavs' championship win, entered Tuesday's game averaging 8.8 points on 33.7 percent shooting (35.8 percent from 3).
He previously missed five games because of knee and ankle injuries this season.
Cavs coach Tyronn Lue said he was unsure of how Smith injured his thumb, however Cavs broadcast partner Fox Sports Ohio reported it occurred when Smith swiped down on the Bucks' Giannis Antetokounmpo.