Arteta and William Saliba had been due to address the media at 6pm UK time but the chartered flight had still hadn't taken off an hour later.
Football.London reports the Gunners were due to take off at 4:15pm UK time but have been waiting in the airport terminal for nearly four hours due to stormy conditions near Luton Airport.
As the cancellation of the press conference was out of Arsenal's hands, the club will not receive a punishment from UEFA. It is also their first offence, meaning they would only be handed a warning anyway.
Newcastle arrived late for their press conference on the eve of their Champions League clash away to AC Milan last month but avoided punishment.
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Among the travelling party were Bukayo Saka - who was passed fit to travel despite limping off injured at Bournemouth on Saturday - and fit-again midfielder Thomas Partey.
Partey had been sidelined since August with a groin injury and the club hoped to have him back for the visit of Manchester City on Sunday.
"He's progressed really well in the last two weeks and he managed to train in the last two or three days with the team and that's great news for us, obviously," Arteta said of the Ghana international.
"I think his progression in the last week has been very good. He might have some exposure tomorrow depending how the game goes."
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Both Arteta and Saliba later spoke to a small number of reporters over the phone and the latter insisted everything would be fine heading into the game.
Asked if he was confident the team would still be at their best, he replied: "Yes, of course. We have to arrive first but tomorrow is another day and we will give our best against Lens.
"It is a really good feeling. My second game in the Champions League with Arsenal. I can't wait to play in France so it is a good feeling.
"We know it won't be an easy game. It is a really good team who finished second last season.
"They didn't start well but in the last two or three games, they are better so we have to be focused on tomorrow and give our best."
Arsenal got their European campaign off to a smooth start with a 4-0 thumping of PSV Eindhoven at the Emirates Stadium. Spanish side Sevilla are the other team in the Gunners' group.