The Ryanair flight was diverted to Stansted Airport where Essex Police officers were carrying out checks.
Two RAF Typhoon Jets escorted the plane which landed at about 18:40 BST.
A spokeswoman for the airline said: "The plane landed normally, but was taxied to a remote stand where passengers disembarked safely."
She said in a statement: "The aircraft and passengers are being checked by the UK police who will decide when they may travel onwards to Dublin on a spare aircraft.
"Passengers in Dublin waiting to depart to Krakow are being transferred to a spare aircraft to minimise any delay to their flight."
Essex Police said: "We have now safely brought off all the passengers from the plane. The plane remains in an isolated area at Stansted and our enquiries are ongoing."