Millar faces up to six weeks out with a hamstring strain while Davidson has been sidelined by a persistent knee problem.
Both players went off injured during St Johnstone's 2-1 home defeat by Aberdeen on Saturday.
Manager Steve Lomas told the club's official website: "It's a blow, that's for sure. Murray saw a specialist last week about his knee which has been bothering him for some time now.
"They don't want to operate and so a mix of rest and electric shock treatment to the affected area to help improve blood supply seems to be the way ahead, but that's going to take time.
"As for Midge, rest and treatment is obviously on the cards but I think we are looking at a significant period of absence."