British Bases spokesman Kristian Gray said the two Brimstone ground attack missiles detached from the aircraft's underwing pods early today.
He said there was no explosion and no one was hurt. An investigation is under way.
Gray didn't specify which mission the aircraft was returning from, but eight Tornado warplanes are now deployed at the base to fly missions against Islamic State group targets in Iraq.
In September of last year, Britain joined the US-led coalition of nations that launched airstrikes against the extremists.
