The group were marched off the plane by police after the jet was diverted to Toulouse, France.
The incident caused long delays for those travelling on the plane.
The flight carried on to the island's capital Palma, but the delay meant the return flight could not leave on time and passengers had to stay overnight.
An airline spokesman said: "EasyJet can confirm that flight EZY6895 from Glasgow to Palma on May 21 diverted to Toulouse due to the disruptive behaviour of a group of passengers on board.
"The safety and wellbeing of passengers and crew is always our priority and upon landing the passengers were escorted off the aircraft by police.
"The aircraft then continued to Palma.
"As a result of the diversion the crew were unable to operate the return flight to Glasgow as it would exceed their legal operating hours. The flight has been delayed overnight and passengers have been provided with accommodation and meals.
"We would like to apologise to passengers for any inconvenience caused by the diversion.
"EasyJet does not tolerate any abusive or threatening behaviour and will always push for prosecution."