Puig has not been cleared to perform baseball activities and wasn't available to pinch-hit in Sunday night's series finale.
"We'll be cautious at this point," Dodgers manager Don Mattingly said. "We think it's going to be OK."
Puig remained in the game after Cardinals starter Joe Kelly hit him in the third inning with an 84-mph changeup, and popped out in foul territory in the sixth. After that at-bat, the team became aware that his hand had become sore, but he was able to play defense and remained in the field through the seventh before Matt Kemp pinch-hit for him in the eighth.
"He hit the next time up and then after that is when [trainer] Stan [Conte] came to me and said it was getting sore," Mattingly said. "That's when we knew he wasn't going to be able to hit the next time."
Puig's injury comes with the Dodgers' offense in a funk. It had scored only 12 runs in 69 innings entering Sunday night's action. Puig has hit .308 this season with 107 hits -- including 12 home runs -- and 52 RBIs.
• Mattingly confirmed again Sunday that starter Josh Beckett is expected to return from the disabled list Tuesday in Pittsburgh. Beckett has a torn labrum and two cysts in his left hip, but expects to pitch through the injury after a cortisone shot.
• Chone Figgins, rehabbing a strained left quad muscle with Triple-A Albuquerque, didn't start Sunday after going 1-for-4 while playing second and third in the two previous games. Mattingly said the plan was for Figgins to likely play nine innings at shortstop Monday.
• With Puig out of the lineup, Scott Van Slyke started in center field Sunday night with Andre Ethier shifting to right field. Mattingly said he chose to keep Matt Kemp, who prefers to play in center or even right, in left field as he hasn't played on the right corner this season.
Alex Halsted is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.