Giants catcher Nick Hundley also received an undisclosed fine.
Unless Puig appeals, he will will begin the suspension on Friday, when the Dodgers play the Seattle Mariners.
Both Puig and Hundley were ejected from Tuesday night's game.
Puig swatted his bat in frustration after fouling off a pitch from Tony Watson, and Hundley said something to the Dodgers slugger while still in his crouch. Puig turned around and walked toward Hundley, the catcher stood up and they stood face to face and argued for a moment before Puig shoved Hundley twice.
That brought players out of the dugouts and bullpens. Puig and Hundley were momentarily separated, but Puig ducked around teammates, coaches and Dodgers manager Dave Roberts before reaching back to hit Hundley. Puig smacked Hundley with an open hand across the front of his catcher's mask.
The Associated Press contributed to this report.