Davis first injured his thumb during Saturday's preseason game against the Brooklyn Nets and was unable to return.
Shams Charania of The Athletic reported Saturday there was no ligament damage, but the additional tests were still necessary to see the extent of the injury. Davis missed Monday's game against the Golden State Warriors.
The Lakers have two more preseason games on the schedule before the regular-season opener against the Los Angeles Clippers on Oct. 22.
Any missed time during the regular season could be devastating for the Lakers, who sent three players and a package of draft picks to acquire the six-time All-Star this offseason. Even with LeBron James on the roster, an injured Davis would leave a massive hole in the rotation.
Meanwhile, Davis could become a free agent next summer, which means the Lakers have limited time to convince the superstar to sign a long-term deal. This could be even more difficult to achieve if the player is forced to spend an extended stretch on the sideline.
JaVale McGee and Dwight Howard will likely see extra playing time while Davis is unavailable.