Fleming was hurt in Monday night's series opener against the Boston Red Sox.
Shortstop Wander Franco had surgery Tuesday for a fractured right hamate bone and is expected to be sidelined for five to eight weeks. Tampa Bay manager Kevin Cash said the team received a report the procedure was "pretty clean."
Injured players also include center fielder Kevin Kiermaier, who is to see a specialist about his ailing left hip after the All-Star break. Catcher Mike Zunino is out indefinitely with a left shoulder injury.
Second baseman Brandon Lowe, sidelined since May 16 with a lower-back injury, was in the lineup for the first of three scheduled games with Triple-A Durham on Tuesday. He will be reevaluated.
For the road team Tuesday, All-Star third baseman Rafael Devers returned to the lineup after missing three games with a sore back as the Red Sox dropped a 3-2 decision to the Rays. The loss also featured the return of Boston ace Chris Sale, who worked five scoreless innings in his season debut.
The Associated Press contributed to this report.