Jalen Suggs of the Magic will miss one game, the league said, for escalating the incident.
The league announced the suspensions Saturday. Bamba will forfeit $284,138 in salary, while Rivers will lose about $60,121 and Suggs will lose $47,740.
Timberwolves forward Jaden McDaniels was fined $20,000 for getting involved in the altercation. Bamba, Rivers, Suggs and McDaniels were all ejected, as was Minnesota's Taurean Prince. The NBA did not give Prince any additional sanction on Saturday.
Bamba and Rivers threw punches during the incident, and the NBA said Suggs and McDaniels "then entered the altercation as non-peacemakers." The league also said Bamba "attempted to continue to engage with Rivers in a hostile manner in the corridor outside the locker rooms where he also aggressively shoved a security representative."
Both Rivers and Bamba had social media posts about the incident, which the league said continued the escalation.