Several drones were shot down overnight on Monday, he said, but "one flew into the same tower at the Moskva City complex" that was targeted on Sunday.
Russia's defence ministry blamed Ukraine for the latest attack.
Kyiv did not comment on responsibility but warned Russia that the conflict could soon move to its territory.
It did not address separate Russian claims that three Ukrainian sea drones were destroyed while trying to attack Russian naval ships in the Black Sea, though did dismiss as "fictitious" further claims that Russian civilian ships had also been targeted.
No one was injured in the skyscraper attack. Moscow mayor said the IQ-Quarter Tower 1 building's "glazing was destroyed over 150 sq m".
The building houses teams from Russia's ministry of economic development, the digital ministry, and the ministry of industry and trade. Staff at the former have been told to work from home, Reuters news agency reports.
Two more Ukrainian drones were shot down by anti-aircraft systems elsewhere in the Moscow region, Russia's defence ministry said, claiming to have thwarted a Ukrainian "terrorist attack".
Moscow's Vnukovo airport was also briefly closed, Russian news agencies reported.
Moscow has repeatedly accused Ukraine of carrying out drone strikes on its territory in recent months, including one on the Kremlin - President Vladimir Putin's official residence in the capital - back in May.
Although Ukraine has not claimed responsibility for specific incidents, Ukrainian President Volodymyr Zelensky has said attacks on Russian territory are an "inevitable, natural and absolutely fair process".
Writing on Twitter on Tuesday, Ukrainian presidential official Mykhailo Podolyak said the conflict would soon move to the territory of the "authors of the war" and bring "more unidentified drones, more collapse, more civil conflicts, more war".
Also on Tuesday, Russia's defence ministry said in a statement that, during the night, Ukraine had made an "unsuccessful attempt to attack the Sergei Kotov and Vasiliy Bykov patrol ships of the Black Sea fleet with three unmanned sea boats".
It said the two ships had been controlling shipping 340 km (211 miles) southwest of the Crimean peninsula and would continue to do so.
Later, in a briefing, the ministry also said three Ukrainian semi-submersible unmanned boats had been destroyed while trying to carry out a "terrorist attack" on Russian civilian transport ships heading towards the Bosphorus Strait.
In response, Mr Podolyak told Reuters: "Undoubtedly, such statements by Russian officials are fictitious and do not contain even a shred of truth.
"Ukraine has not attacked, is not attacking and will not attack civilian vessels, nor any other civilian objects."
He did not respond to the claim that Ukraine had used sea drones to target the Russian navy.
Russia launched its full-scale invasion of Ukraine in February 2022.