The group known as Denaes, which "promotes patriotism" and fights for the "dignity of the Spanish nation", used a fishing boat to tow the block — one of 70 — back to the southern Spanish town of San Roque.
A local judge is now deciding whether the act of removing the block weighing two tonnes was illegal, according to Spanish daily La Vanguardia.
A spokesperson for the British Embassy in Madrid told The Local they were aware of the incident on the part of a group called The Foundation for the Defence of the Spanish Nation.
"The removal of a concrete block is an individual act of vandalism. It is not a violation of British sovereignty," that spokesperson said.
The concrete blocks were at the centre of a diplomatic storm between the UK and Spain in 2013.
Tensions flared in July when boats from the tiny UK-held territory of Gibraltar dumped the blocks in disputed waters used by Spanish fishermen. Gibraltar said it was creating an artificial reef that would boost fish populations and Spain complained the blocks threaten the livelihoods of Spanish fishermen.
Madrid subsequently stepped up border checks, leading to huge queues for motorists, in what Britain and Gibraltar charged were a retaliatory measure aimed at choking the territory's economy.
Spain ceded Gibraltar to Britain in 1713 but has long argued that it should be returned to Spanish sovereignty. London says it will not do so against the wishes of Gibraltarians, who are staunchly pro-British.
The waters off Gibraltar remain disputed.