Manager Alex McLeish was already without skipper Andy Robertson following the Liverpool player’s withdrawal due to dental surgery.
Celtic’s Tierney was set to deputise for Robertson, but will now miss Thursday’s match due to an apparent hip problem, the Scottish Football Association has announced.
Tierney played through a niggle during Celtic’s win over Dundee on Sunday.
The 21-year-old sat out training in an indoor arena in Astana on Tuesday, undergoing some work on his own at the team hotel, but has failed to recover in time.
Robertson missed the team flight to Astana to have treatment on Monday and was told by medical staff that he needs more time for his mouth to settle down.
However, the pair will be available for Sunday’s second Group I qualifier against San Marino.