The 23-year-old Blackburn striker, who has scored nine goals for the Sky Bet Championship club this season, is reportedly suffering from a groin strain.
No replacement has been called up as yet.
Reports suggested Ikechi Anya was struggling with a thigh strain but he trained on Thursday morning and will be fit for Tuesday's match.
Robert Snodgrass has not yet joined up with the squad as his wife is due to give birth but he is expected to report to the national team base at the earliest opportunity.
On Rhodes' withdrawal, Scotland coach Mark McGhee said: "Jordan is a real blow.
"The manager feels a little bit frustrated that he's not been able to give Jordan a real opportunity.
"Jordan might have got that chance this time around and now he's out.
"That's a shame, we would have liked Jordan here but these things happen."