The British warship was reportedly warned it would be fired upon unless it changed course. The dramatic encounter came as tensions continue to mount in the region.
More than 20 Russian aircraft and two coastguard ships were said to be shadowing the HMS Defender.
However, Moscow claimed the Royal Navy ship violated territorial waters near the disputed peninsula and opened warning fires.
The UK Government has rejected Russia’s account of the incident and denied that any warning shots were fired.
A BBC journalist who was on-board the British warship said hostile warnings were being issued over radio by the Russian forces.
One of the warnings issued by the Russians said: “If you don’t change course I’ll fire.”
Moscow boasted that a Su-24 dropped four bombs in the HMS Defender’s path after it refused to back down and claimed that warnings shots were fired from the control ship.
However, the UK Ministry of Defence tweeted: “No warning shots have been fired at HMS Defender.
“The Royal Navy ship is conducting innocent passage through Ukrainian territorial waters in accordance with international law.
“We believe the Russians were undertaking a gunnery exercise in the Black Sea and provided the maritime community with prior-warning of their activity.
“No shots were directed at HMS Defender and we do not recognise the claim that bombs were dropped in her path.”
On Wednesday night, Russia released footage filmed from one of its Su-24M attack jets, showing the HMS Defender sailing off the Crimea.
However, no shots were seen being fired in the footage.
The incident is the first time since the Cold War that Russia acknowledged using live ammunition to deter a NATO warship.
The HMS Defender’s Captain, Vincent Owen, said his mission was confident but non-confrontational and insisted he was maintaining course on an internationally recognised shipping lane.
The BBC’s correspondent on the ship, Jonathan Beale, claimed it was a “deliberate move to make a point to Russia”.