Scan Eagle unmanned aerial vehicle is launched from the USNS Spearhead. AFP
"The drone was shot down just above the fleet headquarters" in the city of Sevastopol, city governor Mikhail Razvojaev wrote on Telegram, blaming the attempt on Ukrainian forces.
"It fell on the roof and caught fire," he said, adding that there was no major damage or victims.
It was the second attempted attack against the fleet headquarters in less than a month.
On July 31 a drone attack in the headquarters courtyard wounded five people and led to the cancellation of celebrations that had been planned for Fleet Day.
It also marked the latest attack to target Russian military infrastructure in Crimea, a Black Sea peninsula that Moscow seized and annexed from Ukraine in 2014.
On Saturday, air defence systems were activated in Evpatoria in western Crimea.
On Thursday, Russian forces shot down a drone near an air base in Sevastopol.
On Tuesday, explosions ripped through a military base and ammunition depot in Crimea.
In early August, a blast at the Saki air base killed one person and wounded several others