The NBA announced the suspension Thursday. Price will miss the Lakers' home game against San Antonio on Friday.
Price hit Rivers in the head with his right forearm early in the fourth quarter of the Lakers' loss at New Orleans earlier this week. Price was ejected for the hit.
Price signed with the Lakers in the offseason, suiting up for his sixth NBA team in 10 seasons.
The Lakers (1-7) are off to their worst start since moving to Los Angeles.