A Monarch spokeswoman said: "It is understood that the flight operating on an Aurela Boeing 737-300 aircraft, registration LY-SKA, with 135 passengers on board left the runway whilst taxiing to the terminal, bringing the aircraft to a stop.
"Passengers have now safely disembarked from the aircraft and have been coached to the terminal where they are being cared for by Monarch airline staff.
"At this time we understand that no passenger or crew have sustained any injuries.
"Monarch apologises to all passengers on board and is offering them all possible assistance.
"Monarch is working with Birmingham Airport to move the aircraft and is fully assisting with the authorities. As a standard precaution emergency services have attended the aircraft."