The airline offered return economy flights to Baku, Azerbaijan, for £979 earlier this month, not including the match ticket.
Supporter Simon Markham claimed his aircraft had been grounded due to a lack of fuel.
He wrote on Twitter: “@ChelseaFC please sort this shambles of a trip to Baku out.
“I know Thomas Cook may be skint but no fuel for the plane? Really?”
Another supporter said: ‘The Chelsea charter flight seems to be stuck on the tarmac at Luton.
“1 hr + delay so far after 1hr 15 mins queue at check in.”
A third added: “We’re still waiting on the tarmac at Luton for fuel, should’ve taken off 75 mins ago, official travel a joke yet again.”
A Thomas Cook spokesman told Daily Star Online: “More than a thousand Chelsea and Arsenal fans are on their way to Baku with Thomas Cook Sport to watch the Europa League Final.
“Two flights from Luton departed nearly two hours later than scheduled due to a delay in getting fuel to the aircraft and air traffic control congestion.
“Customers will arrive in time to soak up the atmosphere and head to the stadium.”
Arsenal and Chelsea received just 6,000 tickets each, despite the stadium having a capacity of just under 70,000.
UEFA said the small alliocation would prevent a huge influx of passengers at Baku.
Two fans have already been injured after an alleged street battle in the Azerbaijani capital.
A British football fan was taken to hospital with a head injury overnight, while another Russian man was hurt in an unrelated incident at a bar.