Rhodes went on as a 68th-minute substitute in place of Leigh Griffiths in Scotland's 2-0 defeat to Group A rivals Belgium on Friday, but hurt his hand and will play no part for Gordon Strachan's side in Skopje.
The 23-year-old has scored four goals in his last two games for Blackburn.
Stoke midfielder Charlie Adam has also been ruled out as he is struggling with a back problem.
- Sports & Recreation
- Gordon Strachan
- Leigh Griffiths