The attack caused a large fire at a Sevastopol shipyard which left 24 people injured, Russia said.
Moscow-installed governor Mikhail Razvozhayev claimed most of the weapons were intercepted.
Russia said two of its ships were damaged as a result of hits by cruise missiles.
A photo shared by Mr. Razvozhayev on Telegram shows flames engulfing what appears to be a vessel at a port as he stands speaking into his phone.
It is thought to be in an area where ships were undergoing repairs. Ukrainian military intelligence sources say a large Russian amphibious landing ship and a submarine - both thought to be in dry dock - were damaged. If both were hit that would make this one of Ukraine's most significant attacks so far on the Black Sea fleet.
The commander of Ukraine's air force, Mykola Oleshchuk, warned there is more to come.
Images circulating on social media, which the BBC has yet to verify, show several large explosions in the area.
The fact that some missiles got through Russia's air defenses and appear to have done substantial damage will be of real concern in Moscow.
Seven of the missiles were downed and all three unmanned boats were destroyed, the country's defense ministry claimed.
IMAGE SOURCE, REUTERS
Image caption,
Smoke lingered in the air the morning after the attack on a Sevastopol shipyard
Russia illegally annexed Crimea from Ukraine in 2014 and this attack shows the tussle for control of the waters. Ukraine has consistently maintained its ultimate goal is to retake the peninsula.
Ukraine has targeted Sevastopol and the Black Sea fleet before but questions remain about which weapons were used in this attack. Western-supplied long-range missiles have been suggested but also Ukrainian-made Neptune missiles could have been used.
Neptune missiles were famously used to sink the Moskva - the flagship of the Black Sea fleet.
Meanwhile, Russian drones reportedly damaged the Ukrainian grain port of Izmail, on the Danube river.
The governor of the Odesa region, Oleh Kiper, said six people had been injured in the attack, which caused a fire and damaged infrastructure.
"Several groups of drones were launched at the Izmail district," Mr Kiper said on Telegram.
"Unfortunately, there were hits: damage to the port and other civil infrastructure was recorded."
