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."
Lomas claimed he needed two or three new players to compete in the SPL this season following the home loss against the Dons, but he has experienced midfielder cover in his squad.
The Northern Irishman said: "Jamie Adams came off the bench on Saturday and we had David Robertson and Kevin Moon not stripped so the absence of Chris and Murray provides opportunities to these players to come in and make an impression."
Saints will also have strikers Gregory Tade and Rowan Vine back from suspension when they face Hibernian at Easter Road on Saturday while Craig Beattie will also be available after illness deprived him of a debut against the Dons.