Johan Lundgren warned the incident “fell well short of the standards that we set for ourselves”.
A co-pilot could be seen completing paperwork with a virtual owl dancing on the screen beside him in video posted by a national newspaper.
Later, he dances next to an animated character with the aircraft said to be flying at 30,000ft during a trip from Paris to Madrid.
Mr Lundgren said: “We have clear policies on how we use social media and that is not part of that policy.
“It was very disappointing. We’re investigating that and for the time being the pilots are suspended.”
Mr Lundgren has issued a warning to all easyJet staff about the importance of using social media responsibly.
“This is causing unnecessary difficulties and it shouldn’t have happened,” he added.
An easyJet spokesman said the video was taken when the aircraft was in cruise control and the flight operated safely.
Mr Lundgren has meanwhile said he wanted easyJet to improve the way it used data to enhance the customer experience, reduce costs and raise revenues.
“I want to make sure that we are leading the way within the airline industry and the world on this because I think there’s nobody out there who really has taken this on to the next step,” he said.
“That’s something I would like to do.”
Mr Lundgren today announced a partnership with manufacturer Airbus to use data analysis to forecast aircraft technical faults before they occur.
This will allow easyJet’s engineers to intervene and replace parts before they cause disruption to flights.
Since joining the airline from tour operator Tui, Mr Lundgren has spent a lot of time “meeting people, listening to people, learning the organisation” as he identifies which of its existing strategies he wants to develop.
“There won’t be any revolution here,” he said. “There will definitely be an evolution. I will supercharge and accelerate some of the things we already do.”
More than half of easyJet passengers will soon be able to book connecting flights through its website as it extends its Worldwide by easyJet service to include more airports and airlines.
The scheme, which is only available for passengers travelling via London Gatwick and Milan Malpensa, allows easyJet passengers needing a connecting flight operated by easyJet or another airline to make one booking that covers the entire trip.
EasyJet is adding Edinburgh, Berlin Tegel, Venice Marco Polo, Amsterdam Schiphol, Paris Charles de Gaulle and Orly airports to the programme from this summer, which means more than half of its flights are included.
It also announced new partnerships with airlines Thomas Cook, Loganair, La Compagnie and Corsair.