The explosion occurred just before 8pm local time on Saturday, close to an Italian restaurant located in one of Moscow's seven Stalin-era skyscrapers at Kudrinkskaya Square, police said.
Russia's Anti-Terrorism Committee said an unidentified woman had tried to get into the restaurant but was stopped by a security guard, the state RIA news agency reported.
It said the woman, the security guard and a customer at the Balzi Rossi Italian restaurant had been killed in the blast that followed.
Those injured received wounds of varying seriousness, the police said. Russia's state RIA news agency released video of heavily armed law enforcement officers at the scene, which had been closed off to the public.
Authorities did not name those killed or injured nor did they say who they thought might have been responsible.
More than four years into a full-scale war with Ukraine, Russia's FSB security service said earlier this year that authorities would step up protection for high-ranking military officials after a series of assassinations and attempted killings it blamed on Kyiv.
The Kommersant daily newspaper cited its own sources as saying that the bomb had been intended to maim and kill guests who were enjoying themselves on the restaurant's summer terrace outside.
It suggested that the bomb had been set off by someone else remotely and that the woman carrying it may not have known that it was an explosive device.
The restaurant's website said the venue had been closed on Saturday for a private event.
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