The pilot on board the F35 ejected from the aircraft before it crashed into the ocean, and has been found safe.
The F35s, estimated to be worth around £100 million each, are on board the £3 billion warship HMS Queen Elizabeth.
Former soldier Tobias Ellwood who chairs the Commons Defence Select Committee, said he had “many questions” about the crash.
The incident happened at around 10am UK time on Wednesday.
An MoD spokesman confirmed: “A British F35 pilot from HMS Queen Elizabeth ejected during routine flying operations in the Mediterranean this morning.
“The pilot has been safely returned to the ship and an investigation has begun, so it would be inappropriate to comment further at this time.”
Jets from the vessel previously participated in strikes against the remnants of the so-called Islamic State in Iraq and Syria.
The 65,000-tonne Royal Navy flagship is returning to the UK from its maiden deployment, which included exercises with the Indian military.
It was part of the carrier strike group’s deployment to the Indo-Pacific amid heightened tensions with China in the region.
The jets are operated by the renowned 617 Squadron, also known as the “Dambusters” squadron.
Foreign Secretary Liz Truss spent time on board the vessel last month on the final day of her two-day visit to India.