Foam jets and dry powder brought the fire under control
More than 100 passengers and crew were on board the aeroplane.
Emergency crews were called to the Essex airport on Wednesday after the Boeing 737 from Dublin landed at 1715 GMT.
Smoke was spotted pouring from the engine of the Ryanair plane by air traffic control staff, who raised the alarm.
'Normal' landing
Essex ambulance crews treated two people at the scene for the effects of smoke, and two others also suffered minor foot injuries.
The aircraft's emergency inflatable slides were used to evacuate the plane.
"As is normal procedure the airport's fire crews were called in and Essex ambulance service was called," said an airport spokesman.
"The aircraft had a perfectly normal landing and after it came to a standstill the fire was put out and the passengers and crew were evacuated."
Passenger Lucinda Conyngham, 33, a film producer from Dundalk, said: "I am very relieved to be down on the ground and just glad that the plane didn't catch fire while we were still in the air.
"Just as we were stopping, people started saying there was a fire and that the engine was on fire.
"Some people were panicking and some people were screaming but generally it was pretty calm. The staff on the plane were very good."
Fellow passenger Martin Murray, 26, a charity worker from Monaghan, said: "You were just thinking that you had to get out and worrying about what might happen if the plane caught fire or filled with smoke."
'Full inspection'
Essex Fire and Rescue Service initially sent in 10 appliances to the scene and they eventually left at about 1800 GMT.
A spokeswoman said: "Foam jets and dry powder extinguishers were used to bring the fire under control."
In a statement Ryanair said the fire, in engine two, happened after the aeroplane was delayed for more than an hour in Dublin when a plastic bag was caught in the other engine.
A spokeswoman said: "The aircraft has been removed from service for a full inspection by Ryanair engineers and relevant authorities.
"We sincerely regret any inconvenience caused to passengers as a result of this incident."
Many of the passengers were put up in hotels in Cambridge before flying on to further destinations on Thursday.