NBA President of Basketball Operations Rod Thorn said the pair had been sanctioned after an incident in the third quarter of the Trail Blazers' 113-101 Saturday victory over Golden State.
Thorn determined Bogut initiated the altercation by elbowing Trail Blazers center Joel Freeland in the jaw.
Six technical fouls were handed out during the fight, with Golden State forward Draymond Green and Williams each ejected.
Williams was set to serve his suspension Monday as the Trail Blazers hosted the New York Knicks while Bogut will miss the Warriors' Tuesday game at New Orleans.
Celebrity Families of 2014 [PHOTOS]