It is the first time that Russia has accused Ukraine of launching an air strike on its territory since Moscow invaded its neighbour on 24 February.
Video images posted online, which have not been verified, showed what looked like several rockets being fired from low altitude, followed by a huge explosion at the oil facility near the Ukrainian border.
The helicopters struck the depot after flying across the border at low altitude, regional governor Vyacheslav Gladkov claimed on messaging app Telegram.
Two workers were injured in the inferno, Gladkov added, while some areas of the city were being evacuated.
There have been repeated fears of Russia launching ‘false flag’ attacks throughout the war, which it could then use as an excuse for escalation.
Belgorod, a city of 69,000 people is 25 miles from the border with Ukraine, and 50 miles from the city of Kharkiv.
Russian oil firm Rosneft, which owns the fuel depot, said no-one was hurt in the fire, though it gave no information on the cause.
Ukrainian officials have yet to respond.
On Wednesday, an ammunition depot near Belgorod caught fire causing a series of explosions.
Gladkov said authorities were waiting for the Russian defence ministry to establish its cause.
It comes as the Ministry of Defence said Russia is redeploying troops from Georgia to bolster its forces in Ukraine after suffering “unexpected losses”.
Between 1,200 and 2,000 of the troops are being reorganised into three battalion tactical groups, according to the MoD intelligence update.
It was “highly unlikely” that Russia had originally planned to use reinforcements in such a way and it was “indicative of the unexpected losses it has sustained during the invasion”, the MoD update said.
Ukrainian forces have recaptured the villages of Sloboda and Lukashivka to the south of Chernihiv, which has been bombarded by heavy Russian shelling, accorind to the defence update.
The villages are located along one of the main supply routes between the city and Kyiv.