Video released by Ukraine's UNIAN news agency showed a dark cloud of smoke rising from the scene after the steel-lattice tower was apparently struck by two missiles during Russia's siege of the city.
The attack briefly caused disruptions to broadcasts but transmissions have been fully restored and the tower is still standing, the deputy head of the presidential office, Kyrylo Tymoshenko, said.
Russia said earlier it would launch targeted attacks on the infrastructure used by Ukrainian intelligence service SBU.
Another air raid siren sounded across the city on Tuesday afternoon and Mayor Vitali Klitschko described the situation as "threatening".
"The enemy wants to conquer the heart of our country. But we will fight and not give up Kyiv," he wrote on Telegram.