Davis has been sidelined by a minor concussion since the middle of New Orleans' second game of the season last Friday night. Rivers has a sprained left index finger and will be out for the first time.
Davis, the first overall choice in the 2012 draft, has averaged 14.5 points, 6.5 rebounds and 1.5 blocks in his first two games.
Rivers has averaged 6 points, 3.3 assist and 2 rebounds through three games, with a season high 9 points in his last game, a victory at Chicago on Saturday night.
Hornets coach Monty Williams says rookie Darius Miller is slated to start at shooting guard in Rivers' absence.