Leonid Parkhomenko was detained Tuesday in the naval port of Sevastopol on the Russian-annexed peninsula.
FSB said the retired second captain had worked in the Black Sea fleet's headquarters and was still a reservist.
Russian television showed FSB-released footage of a handcuffed mustachioed man with greying hair flanked by FSB officers in balaclavas.
He is being questioned as part of an FSB probe into treason and could face up to 20 years in jail.
Kremlin spokesman Dmitry Peskov told journalists that "Ukraine's provocative and destructive activity in Ukraine is continuing, including in Crimea."
Russian special forces "are doing what they have got to do," he said.
Kiev's military spokesman Andriy Lysenko told AFP that Russia's action showed "desperation and lack of professionalism."
The FSB announcement came after Ukraine said on Monday it had captured two of its soldiers at its frontier with Crimea.
Moscow in turn accused Kiev of unlawfully abducting the men from Russian soil.
The FSB earlier this month announced the arrest of a group of suspects whom it accused of planning acts of sabotage in Crimea on the orders of the Ukrainian defence ministry.
Earlier this year, the FSB also claimed it had foiled "terrorist attacks" in Crimea.
Ukrainian President Petro Poroshenko has dismissed the accusations of plotting attacks on Crimea as "fantasies" concocted by Moscow.
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