The club is due to meet Shakhter Karagandy in Astana, the capital city of the former Soviet Republic, in their Champions League play-off tie.
But two travel firms have scrapped plans to take fans to the match and club officials say letters in support of visa applications have been issued to only about 30 fans.
It would mean a round trip of up to 30 hours and at least four connecting flights, with routes including changeovers at Amsterdam, Kiev, Frankfurt, Vienna and Istanbul.
Barrhead Travel has scrapped plans for a supporters' package and so has Milngavie-based Hynds Travel. Manager Iain Hynds said: "It's a logistical nightmare and having just five working days to sort out a visa has made it all the more difficult."
Joe O'Rourke, general secretary of the Celtic Supporters' Association, said the journey, the costs and the need for time off work had deterred fans.