Russia has attacked the power grid and other energy facilities while pressing a battlefield offensive that has left Ukrainian forces on the back foot amid US pressure to secure peace.
Mayor Ihor Terekhov, writing on the Telegram messaging app, did not specify what sort of facility had been hit, but said emergency crews were on the scene and working around the clock.
Kharkiv, just 25km from the Russian border, has been regularly targeted by drones, missiles and glide bombs throughout the war, which enters its fifth year next month.
Regional governor Oleh Synehubov said officials were still trying to assess the extent of damage from Thursday's attack.
Power outages and cuts to heating and water in major cities have worsened over the past week as Ukraine struggles with a cold snap that has overwhelmed the already hobbled energy system.
Kyiv mayor Vitali Klitschko said on Thursday that about 300 apartment buildings in the Ukrainian capital remain without heat after a January 9 attack knocked out heating to half the city's high-rises.
Russia has also stepped up attacks on ports in Ukraine's southern Odesa region.
A missile strike on Thursday injured one person and damaged shipping containers in the city of Chornomorsk, deputy prime minister Oleksiy Kuleba said.
