Their scuffle came with 27 seconds remaining in the second quarter of Oklahoma City's 132-111 victory at Washington on Saturday.
It led to teammates from both sides rushing to help in an altercation that spread into the seating area behind a basket before cooler heads prevailed.
Both players were ejected, as were Oklahoma City forward Jaylin Williams and Thunder guard Cason Wallace for escalating the incident.
Williams was fined $50,000 while Wallace and Wizards forward Anthony Gill were each fined $35,000 by the league for their roles in the melee.
Mitchell, a 23-year-old Belgian, will serve his ban on Monday when the Thunder visit the Philadelphia 76ers.
American Champagnie's suspension will be served on Sunday when the Wizards visit the New York Knicks.
The reigning champion Thunder, on an 11-game win streak, own the NBA's best record at 56-15 while the Wizards, on a 15-game losing skid, are 16-54 with the league's second-worst record.
