Defence Minister Sergei Shoigu said two women, who shot down two of the three drones, will be awarded and given cash bonuses.
The peninsula, seized by Russia from Ukraine in 2014, is home to Moscow's Black Sea Fleet and has been hit by a series of drone attacks since the Kremlin's offensive in Ukraine.
The attack came after President Vladimir Putin made a surprise visit to Sevastopol over the weekend.
Shoigu said three drones attempted to target Russia's infrastructure in Crimea but were destroyed.
The Russian-installed governor Mikhail Razvozhayev said that military personnel had shot at the drones with "small arms" and that "air defence was also working".
Razvozhayev said there were no casualties and claimed no ships had been damaged but added that the explosions blew out windows in several buildings.
Razvozhayev downplayed the attack, saying the navy "confidently and calmly" repelled it.
He urged calm, saying the "situation was under control".
He also dismissed reports that people were leaving Crimea, saying it was a "lie" spread by Kyiv.
"Information is spreading about evacuations from the peninsula by ferry crossings and other such nonsense," he said.
A day earlier Kyiv said Russian missiles were destroyed in a blast in Crimea but denied responsibility for the incident.
In October, Russia's Black Sea Fleet was hit by a major drone attack that the Kremlin blamed on Ukraine.
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