The Zurich based subsidiary of Lufthansa flies to the Greek islands of Santorini, Mykonos, Kos and Crete but the financial crisis that has engulfed the country means that making payments has become more complicated.
Edelweiss pilots now carry a cashbox to pay for “kerosene, handling or landing fees”, pilot Martin Gautschi tweeted in response to a question from the Blick am Abend newspaper.
“The people are very helpful, the service perfect — despite the difficult situation,” Gautschi said.
But he added that all transactions were being conducted in cash “just like in the last days of Swissair”.
In 2001, Swissair became bankrupt and airports would only accept cash for payment of fuel and airport services.
The difference is that Edelweiss, which is this year celebrating its 20th anniversary, is not in financial difficulty but the country of Greece is.
Greek citizens voted on Sunday in a referendum against accepting a proposal from the country's creditors that would have meant more austerity measures.
But the European Central Bank warned on Wednesday that it would cease supporting Greek banks unless the government led by leftist Alexis Tsipras reached a deal by Sunday that was acceptable to the European Union.
The crisis has raised the spectre of Greece leaving the eurozone and a complete collapse of the country's economy.
Residents of Greece are limited to withdrawing €60 a day from bank ATMs, while banks themselves remain closed.
Visitors are not subject to the ATM limits but Greek ATMs have been running out of money so tourists travelling to Greece have been advised to bring cash with them.
Meanwhile, the Schweiz and Sonntag newspaper reported that services such as Moneygram and Western Union had stopped transferring money to Greece until further notice.
That closes off an avenue for people living in Switzerland who may want to send money to relatives in Greece, the newspaper said.