Alvarado also received an undisclosed fine for inciting the incident, according to the league, when he taunted Mets outfielder Dominic Smith after an inning-ending strikeout. Smith and Mets pitcher Miguel Castro also were handed undisclosed fines for their roles in the spat.
Alvarado's suspension was set to begin Sunday night in the series finale against the Mets, but the reliever has decided to appeal the three-game ban.
During the Phillies' 2-1 win over the Mets on Friday, Alvarado thumped his glove and gestured at Smith following the strikeout. While walking back to the dugout, Smith noticed Alvarado's gestures and pulled off his helmet, prompting Alvarado to toss his glove to the ground.
The players appeared ready to fight until both teams spilled out of their dugouts and intervened in the dustup before punches were thrown.
"I don't mind people pimping strikeouts and pimping stuff on the field. I've never been a player like that, but I don't mind it. I love it," Smith said after the game. "But him pointing at me, coming after me, stuff like that -- I'm a grown-[expletive] man. Come meet me then if you really got a problem, and we can really handle it.
"That's how I look at that issue. He waited for his team to grab him and stuff. But I'm right there. He can meet me in the tunnel tomorrow if he really wants to get after it."
In 19 games this season, Smith has a .222 batting average with two home runs and eight RBIs.
Alvarado has a 2-0 record and 1.13 ERA over nine appearances this season.