Beverley, who had five points and five rebounds in 22 minutes before leaving in the third quarter, will be evaluated Thursday.
Beverley has dealt with minor injuries already this season. He sprained his wrist during a Dec. 28 loss against the Utah Jazz and sat out the next three games.
In a Jan. 21 victory over the Dallas Mavericks, Beverley sat out the second half with a strained right groin. The 31-year-old was forced to miss Los Angeles' next three games while recovering.
The Clippers have had to navigate a number of injuries to key players this season. Paul George has missed 21 games due to shoulder and hamstring issues, and Kawhi Leonard has sat out 12 games primarily due to load management and knee injuries.
Head coach Doc Rivers has been able to work around those absences, leading the Clippers to the second-best record in the Western Conference (36-15). Their roster is deep enough that it can overcome periods of time without their best players.
Beverley's absence will allow Lou Williams and Landry Shamet to get more time on the court for the Clippers. Shamet stepped up in Beverley's absence with 23 points in 32 minutes versus Miami.