Young, the Lakers' leading scorer this season at 16.4 points a game, will miss the team's game against the Celtics on Friday in Boston.
The incident occurred with 7:33 left in the second quarter and the Suns leading by one point, 36-35. After Young was fouled on a breakaway layup by Len, he was ruled to have thrown at least one punch as he first engaged Len and later tussled briefly with Goran Dragic.
The Celtics (14-26) announced Thursday they expect to have point guard Rajon Rondo back in the lineup Friday. Rondo injured his right knee last January.
While there was some concern within the Lakers' organization Jordan Hill would also be scrutinized for leaving the bunch during the skirmish in Phoenix, the team's forward-center escaped without any punishment.