The so-called October 22 splinter group of the National Liberation Front of Corsica (FLNC) made the announcement during a nighttime news conference at a location unknown to the six journalists present, in line with FLNC practice since its formation in May 1976.
It said its decision was to allow the island's new assembly, led by nationalists, "to fulfil its mandate calmly".
However, the spokesman said: "The end of military operations does not mean a laying down of weapons."
The main FLNC movement known as the Combattants Union (UC) had announced in June 2014 that it planned to end its armed struggle.
The FLNC, which was set up in 1976, and various other factions intent on self-rule staged hundreds of attacks in Corsica.
They demanded the recognition of the "national rights of the Corsican people", including citizenship, language and culture.
There have been thousands of attacks in the 40-year struggle during which nine police officers have been killed.
The FLNC has also been blamed for armed robberies and extortion through so-called revolutionary taxes.
But the group suffered from internal feuds in the 1990s, a decade when it also staged the assassination of Claude Erignac, the prefect of Corsica and the island's top official.
Lying in the Mediterranean, Corsica was conquered by the French in the 18th century and was the birthplace of Napoleon Bonaparte.
Nowadays, the island of around 300,000 people is a popular tourist destination, famed for its spectacular beauty and climate.