The main headquarters of Russia's Black Sea Fleet was on fire on Friday after being hit by a Ukrainian missile.
At least one Ukrainian missile struck the building, Sevastopol governor Mikhail Razvozhayev wrote on the Telegram messaging app.
The peninsula was also hit by an attack targeting its internet providers, an official from Crimea's Russian-backed administration said.
“Unprecedented cyberattack on Crimean internet providers. We are fixing internet outages on the peninsula. All services are working to eliminate the threat,” said Oleg Kryuchkov, an adviser to Crimea governor Sergei Aksyonov.
Mr Razvozhayev told locals to avoid the centre of Sevastopol, where the Russian Navy building is located.
Firefighters were at the site and some roads were closed, he said.
“The headquarters of the fleet have been hit in an enemy missile attack,” he said, adding that missile fragments had fallen near a theatre.
In a second post, Mr Razvozhayev warned that another Ukrainian aerial attack could be imminent, urging residents of Sevastopol – which has a population of more than 500,000 – to remain indoors.
“Attention everyone! Another attack is possible. Please do not go to the city centre. Do not leave buildings,” he said.
“Everyone who is near the headquarters of the fleet – at the sound of the siren, proceed to shelters.”
Crimea has been the target of Ukraine throughout Russia's offensive, but attacks have recently intensified as Kyiv vows to recapture the Black Sea peninsula, which Moscow annexed in 2014.
Authorities said air defences downed another missile on Friday, near the town of Bakhchysarai, just outside Sevastopol. Mr Aksyonov said “cruise missiles” had been downed over the peninsula.
Ukraine confirmed its strike on Moscow's naval command base on the peninsula, which Kyiv has vowed to take back since it was annexed by Russia in 2014.
"Ukraine's defence forces launched a successful attack on the headquarters of the command of the Black Sea Fleet of Russia in the temporarily occupied Sevastopol," the Ukrainian army said on Telegram.
One person was killed and 15 injured on Friday in a Russian missile strike on the central Ukrainian city of Kremenchuk, said Dmytro Lunin, governor of Poltava region.
Mr Lunin said earlier that Russia had hit civilian infrastructure with missiles. Ukrainian Prime Minister Denys Shmygal also said Russia has restarted a systemic campaign of aerial strikes on energy infrastructure.
Earlier this week Russian troops hit an oil refinery in Kremenchuk but it was not immediately clear what was the target on Friday.
"One missile was shot down by air defense forces. All relevant services are working at the scene," he said.
This came as Ukraine's President Volodymyr Zelenskyy met US President Joe Biden and Congress leaders in Washington. Mr Biden has asked Congress to provide an additional $24 billion in military and humanitarian aid for Ukraine.
Last week, authorities in Sevastopol accused Ukraine of attacking a strategic shipyard in the city, damaging two ships undergoing repairs and causing a fire at the centre.
Meanwhile, in the southern region of Kherson, shelling killed one person and wounded another, governor Oleksandr Prokudin said on Friday.