Russian-installed Governor Mikhail Razvozhaev said the second attack was repelled over the sea off the peninsula.
He called for calm and said no damage had been caused.
"The Ukrainian Nazis have again tried to attack our thermal power station at Balaklava," Razvozhaev said on Telegram, referring to a facility near Sevastopol, the home port of Russia's Black Sea naval fleet.
"Our fleet also repelled an attack offshore by three UAVs (unmanned aerial vehicles)."
Razvozhaev said the city of Sevastopol was now quiet "but all services and forces are in a state of military readiness".
Russia blamed Ukraine for an attack on the port using air and marine drones at the end of October, in response to which it briefly suspended its participation in a deal to facilitate the export of Ukrainian grain via the Black Sea.
In an earlier posting, Razvozhaev said an attack by drones was underway.
Air defences were working and two drones had been shot down.
Crimea was one of the launch pads for Russia's invasion of Ukraine on February 24 and has several times come under attack - most spectacularly in August when a series of explosions destroyed a group of warplanes at a Russian naval base.
Ukraine's government on Tuesday urged people to conserve energy amid relentless Russian strikes that have halved the country's power capacity, as the United Nations health body warned of a humanitarian disaster in Ukraine.
Authorities said millions of Ukrainians, including in the capital Kyiv, could face power cuts at least until the end of March due to the missile attacks, which Ukraine's grid operator Ukrenergo said had wreaked "colossal" damage.
Temperatures have been unseasonably mild in Ukraine this autumn but are starting to dip below zero and are expected to drop to minus 20C or even lower in some areas during the northern hemisphere winter months.
Russia's attacks on Ukrainian energy facilities follow a series of battlefield setbacks that have included a pullout of Russian forces from the southern city of Kherson to the east bank of the mighty Dnipro River that bisects the country.
"Saving electricity remains critically important," Prime Minister Denys Shmyhal said on Telegram on Tuesday.
Planned power shutdowns are happening in all regions, and emergency shutdowns are possible in some situations as frosts have started and electricity consumption is rising, he said.
The World Health Organisation said hundreds of Ukrainian hospitals and healthcare facilities lacked fuel, water and electricity.
"Ukraine's health system is facing its darkest days in the war so far. Having endured more than 700 attacks, it is now also a victim of the energy crisis," Hans Kluge, WHO's regional director for Europe, said in a statement after visiting Ukraine.
Meanwhile, Ukraine on Tuesday received a new 2.5 billion euro ($A3.9 billion) tranche of financial support from the European Union, Finance Minister Serhiy Marchenko said.
US Treasury Secretary Janet Yellen said disbursement of $US4.5 billion ($A6.8 billion) in US aid for Ukraine would begin in the coming weeks to bolster its economic stability.
Ukraine's SBU security service and police raided a 1000-year-old Orthodox Christian monastery in Kyiv early on Tuesday as part of operations to counter suspected "subversive activities by Russian special services," the SBU said.
The sprawling Kyiv Pechersk Lavra complex - or Monastery of the Caves - is a Ukrainian cultural treasure and the headquarters of the Russian-backed wing of the Ukrainian Orthodox Church that falls under the Moscow Patriarchate.
Russia's Orthodox Church condemned the raid as an "act of intimidation".
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