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.
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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.
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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.
WATCH: Houston Astros players, including Jose Altuve, Justin Verlander, Carlos Correa, Alex Bregman, apologize for cheating scandal
Houston Astros players apologize for cheating scandal