Kempe scored a goal and added an assist in Monday's 3-0 win over the Predators.
Kempe delivered two assists, including one on the power play, in a 3-2 win over Utah on Saturday.
Kempe scored a goal on a team-high three shots in Wednesday's 4-3 loss to Edmonton.
Kempe (upper body) will be a game-time decision versus Dallas on Saturday, according Zach Dooley of the Kings' official site.
Kempe (upper body) is week-to-week but expected to return before the end of March, Darren Dreger of TSN reports Thursday.
According to Austin Stanovich of The Hockey News, Kempe (upper body) won't play Tuesday against Calgary after flying back to LA to undergo tests on an injury he sustained Monday versus Edmonton.
Kempe logged a power-play assist, seven shots on goal, two PIM and a minus-2 rating in Thursday's 4-1 loss to the Predators.
Kempe failed to score a goal against the Capitals on Wednesday despite seven shots on net.
Kempe scored a goal on eight shots and added four PIM in Thursday's 4-3 overtime loss to the Penguins.
Kempe scored twice on nine shots, dished a power-play assist, went plus-2 and added 10 PIM in Saturday's 4-3 loss to the Avalanche.