This was the early flight from London Gatwick that was the first to land at Skiathos Airport at 11.30am.
The Berlin-based airline, which flew to destinations across Europe, Africa and the Middle East, transported more than four million passengers a year.
It blamed rising fuel prices and currency fluctuations as two factors.
"We ultimately failed to successfully complete our financing efforts to meet short-term liquidity needs," said managing director Karsten Balke.
"We very much regret that, as a consequence, we had no choice but to file for bankruptcy."
The company said that passengers who had booked flights as part of a package should contact their tour operator to make different arrangements, but added that people who booked directly with them were not entitled to a replacement flight.