Gunners recorded a 1-0 victory in Harare on Saturday but the chances of the team even lining up on the pitch for the second leg of the second round tie appear remote.
"We don't have the money to go to Cairo to fulfill the second leg of the tie and when you have no money it means that you can't fly," team owner Cuthbert Chitima told the state-owned Herald newspaper.
"It has been a beautiful campaign, and we have enjoyed it and given the nation a big boost with our success, but it has come at a huge cost to us financially and we are a very young club and can't afford it."
The victory meant the Gunners, who won Zimbabwe's championship last year in only their second season in the premier league, became the first Zimbabwean club to beat the fabled Egyptian club in nine attempts.
Zimbabwe has been in an economic crisis for a decade with the government last year adopting use of multiple foreign currencies to replace a Zimbabwe dollar rendered worthless by hyper inflation.
Western donors have held back aid crucial to rebuilding the economy as rival factions continue to jostle for power in the southern African country.
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