Both were injured last weekend at Tennessee.
Davis left less than three minutes into the game with a left knee injury. Fleener left just before halftime after hurting his left shoulder.
Arians says he hopes both starters will return to Indy's lineup in a couple of weeks.
Fleener was a second-round draft pick and one of Andrew Luck's college teammates at Stanford before coming to Indy. He is third on the team with 21 receptions.
Indy traded two draft picks to Miami to acquire Davis late in the preseason. He has 19 tackles in five games and missed two games with an ankle injury.