The pilot ejected and was safely returned to the carrier, the UK Ministry of Defence confirmed.
The accident happened at about 10am UK time in international waters. The F-35, which is made by US manufacturer Lockheed Martin and is believed to cost £100 million, has yet to be recovered.
An investigation is now taking place into the incident, with human or technical error likely to blame. Hostile action is not thought to have been involved.
A Ministry of Defence official said: “A British F-35 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.”
The HMS Queen Elizabeth was deployed to the Middle East earlier this year and has spearheaded a mission against ISIS targets in Syria and the wider region. It was returning to the UK when the accident occurred.
The £3 billion ($4.25bn), 65,000-tonne aircraft carrier has eight advanced British F-35 jets on board, along with 10 US F-35s.