The blast on Saturday evening at the Balzi Rossi, an upscale Italian establishment in central Moscow, killed three people including the woman bomber, Russian state media said, citing local officials.
"Yesterday, a brutal terrorist act was committed in Moscow that claimed human lives. The victims are currently in the city's hospitals, where they are receiving all necessary care," Sobyanin wrote on social media on Sunday.
He added that a probe into the attack was underway.
"Those responsible for committing this crime will certainly be found and will face the punishment they deserve," he wrote.
At least 21 people were wounded when the explosive device detonated at the restaurant on Kudrinskaya Square, the National Anti-Terrorism Committee said late on Saturday, according to Russian state news agency Ria Novosti.
A woman attempted to smuggle the bomb into the establishment but a security guard refused to let her in before the bomb exploded, Ria Novosti reported.
The Moscow Investigative Committee said on Saturday evening the attack was still being investigated.
As of early afternoon on Sunday, there was no further information from Russian authorities and no one had publicly claimed responsibility.
According to Ria Novosti, the restaurant was closed for a private function on Saturday evening.
Footage released by Russian state media showed heavily armed law-enforcement officers, several ambulances and other emergency vehicles at the site.
Earlier this year, Russia's Federal Security Service announced that authorities would tighten security around senior military and government officials, after a series of assassination attempts in Russian cities that followed the Kremlin's full-scale invasion of Ukraine in February 2022.
So far, Russian authorities have not drawn any connections between Saturday's blast and these earlier attacks or the war in Ukraine.
Russia previously said Ukraine was behind a car bombing in Moscow last April that killed Lieutenant General Yaroslav Moskalik, a deputy head of the main operational department in Russia's General Staff.
Ukraine did not publicly claim responsibility.
But Ukraine's SBU security service earlier said it had organised the killing in December 2024 of Lieutenant General Igor Kirillov, who headed the Russian military's nuclear, biological and chemical protection forces.
Kirillov was killed by a bomb hidden in a scooter outside his apartment building in Moscow, a day after Ukraine's security service levelled criminal charges against him.
Among other prominent victims of bombing attacks in Russia were Daria Dugina, the daughter of influential nationalist thinker Aleksandr Dugin, and Vladlen Tatarsky, a well-known pro-Kremlin military blogger.
Ukraine denied involvement in the attack on Dugina and did not respond to Russian accusations that it was behind Tatarsky's death.
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