Ukrainian officials say 10 people have been injured in the attack on the eastern border city.
Ukraine’s national police said the attack early on Saturday was launched by drones. It published pictures of blazes that had broken out on city streets and next to buildings.
“As of this morning, there are 6 dead and 10 wounded as a result of the night strike on Shevchenkivskyi district,” Kharkiv Mayor Igor Terekhov said on the Telegram messaging app.
“The attack hit residential areas – at least nine high-rise buildings, three dormitories, a number of administrative buildings, a shop, a petrol station, a service station and cars were damaged,” he said.
Photos released by police on Telegram showed several fires in civilian areas, including near a residential high-rise. The strike took place just after midnight, according to local news reports.
Ukraine’s military said on Facebook that its air defences destroyed 28 of 32 drones and three of six missiles launched by Russia.
Meanwhile, police said there were no casualties in a separate attack on Mala Danylivka, a village on Kharkiv’s northwest outskirts.
Air raid alerts remained in effect for Kharkiv and most of the country, including the capital Kyiv, for several hours after the strikes.
Kharkiv, the capital of the region of the same name, lies just 30km (19 miles) from the border with Russia and has come under frequent bombardment since Moscow launched its invasion in February 2022.
The attacks have intensified in the past few weeks. On Wednesday, a drone attack on the city killed four people and badly damaged apartment blocks.
President Volodymyr Zelenskyy’s chief of staff, Andriy Yermak, told the news outlet Politico in an interview published on Thursday, that he saw Kharkiv as the most likely target for any new Russian offensive in May or June.
Ukrainian officials have urged the country’s allies to supply more anti-aircraft defence systems, in particular modern US-made Patriot systems.
US military aid to Ukraine has been drying up, with a $60bn funding package currently stalled in Congress, amid fierce opposition from Republicans.