The bizarre incident occurred as the passengers tried to board Wizz Air flight number W6 1614, which was due to depart for Gdansk in Poland at 11.10pm on Tuesday.
They handed over their boarding passes and walked down a flight of stairs to an electronically controlled door which leads to where the aircraft was parked.
The door was locked so they waited for 20 minutes for ground crew to open it.
They became concerned when it appeared the aircraft was finished boarding and was preparing for take-off.
The stranded passengers walked back upstairs to find a deserted departures area.
All the lights had been switched off and all the doors were locked.
They began banging on doors as their flight took off without them.
Airport cleaning staff had to rescue them, triggering an alarmed door, resulting in a response from airport police and fire service.
Ania Sztandke, whose husband, Maciej Malkiewicz, was among the stranded group, criticised the airport and the airline.
“I rang and nobody knew about the incident. I rang Wizz Air and they didn’t know either. I think it’s a joke,” she said.
“What about safety procedures? What if someone passed out on the way to the plane? It’s funny, because they can stop the flight if there is an aggressive or drunk passenger, but they can’t when they forget about some passengers.”
A spokesperson for Wizz Air confirmed that it is investigating the incident.
In a statement, she said the aircraft took off “with the report from ground handling that all the passengers were boarded”.
“After take-off, the captain was informed 21 passengers were not boarded on the aircraft — possibly because a timing mechanism on the gate of the terminal activated, therefore the gate closed before the last 21 passengers could go through.
“It is still under investigation with airport police and access control [checking] why the gate closed,” she said.