All 151 passengers on the flight from Ljubljana, in Slovenia, were evacuated down emergency chutes after the pilot took the decision to make an unscheduled landing at Cologne-Bonn airport, in Germany, at around 5pm on Saturday.
Three men were arrested after every passenger was made to leave the plane and undergo a security check.
A Cologne police statement said: "During the flight, other passengers had made the crew aware of the men.
"According to the witnesses, these had been the subject of terrorist content.
"Thereupon the flight captain had decided to carry out an evacuation in Cologne around 6pm (local time).
"There, the machine was cleared in a secure area via emergency slides.
"The three suspects were arrested. Officials of the federal police ensured a backpack in the passenger area to be assigned to the men.
"This was inspected outside the aircraft by a defiler and was blown up in a controlled manner."
The police statement added the three men were being interrogated and they were investigating "on the suspicion of the preparation of a serious state-threatening violence".
A spokesman for Cologne-Bonn airport said the pilot took the decision to land the plane.
"Prior to this, the pilot had been informed about a suspicious conversation on board, after which he decided to make an unscheduled landing in Cologne-Bonn.
"After the safe landing of the aircraft of the type A319, the 151 passengers left the machine via emergency slides and were taken to a transit gate.
"The police have been informed and have taken action.
"Thus, passengers had to undergo a check immediately after landing."
Flights were suspended at the airport for three hours.
An easyJet spokeswoman said: "easyJet can confirm that flight EZY3246 from Ljubljana to London Stansted diverted to Cologne on Saturday.
"The captain took the decision as a precaution to enable the aircraft to go through additional security checks in Cologne where the aircraft was met by the police.
"In compliance with the local authorities' guidance, passengers disembarked to allow additional security checks to be performed."
She added the passengers had been given a hotel stay for the night and would fly back on Sunday morning.
"We thank passengers for their understanding," she said.
"The safety of easyJet's passengers and crew is our highest priority."