Thompson underwent an MRI on Wednesday morning and did not travel to Boston for a critical game against the Celtics. He was injured during Tuesday night's 122-102 victory over the Orlando Magic.
The Cavaliers said he will not play in the next two games while receiving treatment before being reevaluated.
"X-rays taken at the arena following the game were negative. Thompson did not travel with the team to Boston last night in order to have additional evaluation and imaging done at Cleveland Clinic this morning," the team statement said Wednesday. The results have confirmed a sprained right thumb. He will miss (Wednesday's) game in Boston vs. the Celtics and Friday in Cleveland vs. the Hawks while undergoing continued treatment and additional evaluation. His status beyond that will be updated as appropriate."
Thompson's streak of 447 consecutive games played will end as the Cavs face the Celtics with first place in the Eastern Conference and a tiebreaker on the line. They are both 50-27.
The 6-foot-9, 238-pound Thompson, who had not missed a game since Feb. 10, 2012, is averaging 8.1 points and 9.3 rebounds this season. His streak is a franchise record and the longest active streak in the NBA.
The Cavs recalled center Larry Sanders from from the Canton Charge of the NBA Development League as he continues to work his way back into playing shape.
Sanders, 28, had not played in the NBA since the 2014-15 season before signing with the Cavaliers on March 13 to provide frontcourt depth following Andrew Bogut's season-ending left leg injury.
Sanders has played in four games for the Charge this season with averages of 6.0 points, 8.0 rebounds and 2.5 blocks in 19.4 minutes per contest.
Since signing with the Cavs, the 6-11, 230-pound Sanders has appeared in two NBA games. He committed two fouls in two minutes in his season debut March 14 against Detroit and played another two minutes on March 25 against Washington.