The Hadron Collider was designed to recreate conditions seen after the Big Bang
The man, who has not been named, is suspected of having links with a terrorist organisation based in Algeria.
The European Nuclear Physics Organisation said the man was arrested on Thursday by French police.
The lab says the suspect was working under contract with an external institute.
It said he had no contact with anything that could have been used for terrorism.
Police in the Isere department of France made no immediate comment on reports of the arrest.
The European laboratory specialises in high-energy particle physics and has been working for years to build the world's biggest atom smasher.
The Hadron Collider, buried 100m under the ground near Geneva, Switzerland, is supposed to recreate conditions seen after the Big Bang, the event that many scientists believe gave birth to the universe around 14 billion years ago.
The £4.4bn machine fires protons round a 17-mile-long tunnel at close to light speed in order to smash them in to each other.
