Essex police said they conducted "routine breath tests" on both pilots after the incident today morning but there were no signs of alcohol. They said no further police action is planned.
Ryanair spokesman Robin Kiely said the wing tip of one plane and the tail cone of another "made contact" while one plane was approaching the stand and the other was pushing back.
He said passengers were put on other planes after a three-hour delay.
Airport spokesman Chris Wiggan said both planes were damaged and the Air Accident Investigation Board is handling the inquiry.