Ukraine's military, which has accused Russia of killing many civilians in its own attacks on Ukrainian cities, did not immediately respond to an emailed request for comment.
Vladimir Saldo, the Russian-installed governor of the region, first made the accusation about the strike in a statement.
Russia's foreign ministry and senior Russian politicians later accused Ukraine of carrying out "a terrorist attack".
Reuters was not able to immediately verify photographs of what Saldo's press service said was the aftermath of the attack or the allegation.
At least one dead body was visible in the images beneath a white sheet.
The building showed signs that a fierce fire had raged and there were what looked like blood stains on the ground.
Saldo said in his statement that three Ukrainian drones had struck the site of New Year celebrations in Khorly, a coastal village, in what he said was a "deliberate strike" against civilians.
He said that many people had been burnt alive.
Russia's foreign ministry said initial information indicated that 24 people, including one child, had been killed, and that 50 people had been injured, including six minors who were being treated in hospital.
"There is no doubt that the attack was planned in advance, with drones deliberately targeting areas where civilians had gathered to celebrate New Year's Eve," the ministry said in a statement, calling the attack "a war crime".
Dmitry Medvedev, deputy chairman of Russia's Security Council, told the TASS state news agency that Russia would seek its revenge on the battlefield and said that those who carried out the attack and their commanders should be targeted.
Russian foreign ministry spokeswoman Maria Zakharova said in a statement on Telegram that Ukraine's allies were ultimately to blame.
Senior politicians, including the speakers of both houses of Russia's parliament, condemned Ukraine.
Kherson is one of four regions in Ukraine which Russia claimed as its own in 2022, a move Ukraine and its allies have denounced as an illegal land grab.
Ukrainian President Volodymyr Zelenskiy said on Thursday a Russian drone attack damaged power infrastructure in several Ukrainian regions overnight.
"On New Year, Russia deliberately brings war. Over 200 attack drones were launched onto Ukraine in the night," Zelenskiy wrote on Telegram.
Zelenskiy said energy infrastructure in seven regions across Ukraine had been targeted.
He met with US President Donald Trump in Florida on Sunday to negotiate a peace framework to end the nearly four-year war.
Both leaders have said they are close to an agreement but thorny issues around post-war control of territories remain.
The Ukrainian energy ministry said a "significant number" of households in the Volyn and Odesa regions - in northwestern and southwestern Ukraine respectively - were disconnected from power supplies by the overnight strikes, as well as some in the Chernihiv region north of the capital Kyiv.
The governor of Volant said more than 103,000 households in that region had lost power as a result of the attack.
Volyn region is several hundred kilometres from the front line and borders NATO military alliance member Poland.
