The Scottish Football Association confirmed just ahead of manager Gordon Strachan's media conference that Dorrans was out through injury.
Defenders Christophe Berra and Andy Robertson pulled out on Wednesday.
Strachan confirmed that Darren Fletcher would be his captain. Scott Brown wore the armband during Fletcher's long absence through illness, but the Celtic midfielder is out with a hamstring problem.
Strachan said of the Manchester United midfielder: "It's great to have his enthusiasm and his experience. You can tell the players enjoy him being here and more so he enjoys being here."
Strachan had already called up Aberdeen defender Mark Reynolds in anticipation of Berra pulling out with his knee injury and he will not replace Dorrans or Robertson, who pulled out with a calf problem. The Scotland boss has Steven Whittaker and Derby left-back Craig Forsyth vying for a place at left-back.
On Dorrans, Strachan said: "He has been playing with an injury the last few weeks.
"It was great he came up here and gave it a couple of days' rest and tried to train yesterday, but he wasn't comfortable, so he is away back to his club now to get assessed.
"They know what it is, you would need to ask them how long it's going to be."
On his missing defenders, Strachan said: "That's a blow. Both of them have been doing well. Christophe has been scoring goals as well. But his injury was bad enough not to allow him to travel.
"Andy came up and tried his best. We felt it wasn't worthwhile pushing it because he couldn't train.
"We are okay, we are happy with the training we have done. Everybody else has been involved.
"We picked a few extra players because we knew we might get some knocks, so we are well covered."