Walter Smith says Chris Burke and Steven Naismith are unlikely to play again until next month at the earliest.
The duo were both stretchered off in the weekend's Scottish Cup semi-final win over St Johnstone at Hampden.
Naismith has a knee problem whilst Burke is suffering from an ankle injury, and both are undergoing further checks.
Smith was quick to confirm that neither would feature against Fiorentina in the first leg of their Uefa Cup semi-final on Thursday.
"Naismith and Burke have no chance of playing on Thursday and I think they will miss our next three games at least," he told the club's website.
"That is only an early diagnosis and we will have to wait and see what the specialists say about them.
"At this stage, it doesn't look like they will be able to feature in either the Fiorentina games or against Celtic this coming Sunday."
Naismith and Burke have joined the list of absentees for the clash with Fiorentina.
Barry Ferguson and Kevin Thomson are both suspended, whilst Allan McGregor, Lee McCulloch and Charlie Adam are injured.