Both are appealing.
MLB handed down the suspension Tuesday, less than 24 hours after the benches-clearing incident.
Strickland was suspended and fined an undisclosed amount for what MLB Chief Baseball Officer Joe Torre said was “intentionally hitting Harper with a pitch, inciting the bench-clearing incident and fighting.”
In addition to the suspension, Harper was fined an undisclosed amount for “charging the mound, throwing his helmet and fighting,” according to Torre.
Strickland plunked Harper in the hip with a 98 mph fastball. Harper then gestured at Strickland with his bat, strode to the mound and threw his helmet at the Giants pitcher before the two exchanged blows as the benches cleared.
“You either go to first base or you go after him, and I decided to go after him,” Harper said of his decision to charge the mound.
It was the first time the two had met since Harper hit two home runs off Strickland during the 2014 National League Division Series between the Nationals and Giants.
Both players were ejected from the game. It was the first time Harper had been tossed for fighting in a game.
Harper was starting in right field for Washington on Tuesday night.