Kelly triggered a bench-clearing confrontation during the Dodgers' 5-2 victory over the Astros on Tuesday in the first meeting between the two teams since Houston were punished for their 2017 sign-stealing scandal.
A statement from Major League Baseball said Kelly had aimed a pitch near Astros shortstop Alex Bregman's helmet, and later taunted Carlos Correa after striking the Houston slugger out in the sixth inning.
Kelly's exchange with Correa prompted players from both benches to stream onto the field at Minute Maid Park in a tense standoff before calm was restored.
Kelly has appealed the suspension, meaning he is free to play until the case is settled.
Dodgers manager Dave Roberts was also given a one-game suspension for his role in the confrontation. Astros manager Dusty Baker, who was caught on microphone swearing at Kelly, has been fined an undisclosed amount.
Tuesday's clash between the Astros and Dodgers was a rematch of the 2017 World Series, which the Astros won in seven games.
That World Series victory however was later tarnished by revelations that the Astros had used an elaborate system to steal the signs of opposing pitchers using cameras hidden in the outfield.
The scandal stunned the world of baseball, and ultimately led to the suspension and dismissal of general manager Jeff Luhnow and field manager A.J. Hinch.
The Astros were also fined $5 million (4.24 million euros), the maximum allowable under MLB rules.
MLB commissioner Rob Manfred resisted calls to strip the Astros of the title however, and also failed to levy punishments against multiple Houston players who admitted their part in the cheating plot.
Speaking to reporters on Wednesday, Dodgers skipper Roberts said he would warn his players not to leave the bench again, emphasising the potential risks of confrontations in the era of COVID-19.
"I'm going to talk to the guys today briefly about leaving the bench. MLB is really serious about this, as well as they should be. I have to reiterate it to guys, at any cost, to stay on the bench," Roberts said.
However Roberts, who won't appeal his one-game ban, sympathised with the lingering frustration of his players over the Astros cheating scandal.
"This is something that has built up over the course of seven months after the findings," said Roberts.
"It sort of released. It was unfortunate, but to spin it, it's a good thing we got it out of the way and move on and play baseball."
Meanwhile, the second game of the Dodgers' road series in Houston passed off without incident on Wednesday.
A two-run homer from Edwin Rios in the 13th inning sealed a 4-2 victory for the Dodgers, who improved to 4-2 in the National League West standings.