Stuart Armstrong and Christophe Berra have withdrawn for the Scotland squad for the Euro qualifiers against Georgia and Germany.
Armstrong, 23, will have to wait to win his first Scotland cap after missing Celtic's 3-1 win over St Johnstone with a back injury.
"I think he will be out for the games because he has an injury in his back," said Celtic boss Ronny Deila.
Berra, 30, could be out of action for a month after injuring his hamstring.
Armstrong was the only uncapped player in Gordon Strachan's squad.
"It is nothing big but big enough that he will miss the games, I think," added Deila.
"It is something that he has had for a couple of weeks, that is why he has been off the pitch a couple of times.
"So now we have an opportunity to rest him for a couple of weeks and get him 100% again."
|Scotland's remaining Euro 2016 qualifiers|
|Georgia (a)||4 September|
|Germany (h)||7 September|
|Poland (h)||8 October|
|Gibraltar (a)||11 October|
Third-placed Scotland play Georgia in Tbilisi in Group D on Friday and follow that with a home match against world champions Germany at Hampden three days later.
Armstrong's club captain Scott Brown should be fit for the games despite being injured in a tackle with Saints midfielder Chris Millar and being substituted for Charlie Mulgrew in the second half at Celtic Park.
"I think everybody can be calm, he will be ready for Scotland's games against Georgia and Germany," said the Celtic manager of Brown.
"I don't know what the injury is but it is not anything big and serious, it was a hit."
Meanwhile, Germany have announced their squad to play Group D leaders Poland on Friday and for the visit to Hampden.
It includes Bayern Munich goalkeeper Manual Neuer, Manchester United midfielder Bastian Schweinsteiger and Arsenal's Mezut Ozil.
Head coach Joachim Low said of his team who trail the Poles by one point: "I am convinced about the quality within my team and the character of every one of my players.
"We know what needs to be done and now we will move up a gear. We are ready."