Kelly was originally penalized eight games by Major League Baseball on July 29, a day after throwing a 96 mph fastball near the head of Houston's Alex Bregman and two curveballs that brushed back Carlos Correa.
The Dodgers on Wednesday confirmed the reduced penalty that was first reported by Barstool Sports.
Kelly went on the 10-day injured list retroactive to last Sunday with right shoulder inflammation. He will serve his suspension when he returns.
After striking out Corea, Kelly curled his lip into a pouting expression and exchanged words with the shortstop.
Benches cleared after Kelly's actions during the sixth inning of Los Angeles' 5-2 win at Houston in the teams' first meeting since it was revealed the Astros stole signs en route to a 2017 World Series title over the Dodgers.
Dodgers manager Dave Roberts served his one-game suspension the same day the penalty was handed down. Astros manager Dusty Baker was fined an undisclosed amount.
Kelly denied that he purposely threw at the Astros. He has previously been suspended in his career for throwing at a batter.
The penalties were imposed by former pitcher Chris Young, MLB's senior vice president of baseball operations, who issued his first ruling since taking over the job from Joe Torre.
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