Moscow, a city of around 13 million people, has been the epicentre of Russia's coronavirus outbreak. It reported 7,993 new cases on Saturday , up from 6,868 the day before and well above the daily tallies of around 700 seen in early September.
The age for those receiving shots is capped at 60. People with certain underlying health conditions, pregnant women and those who have had a respiratory illness for the past two weeks are barred from vaccination.
Russia has developed two Covid-19 vaccines, Sputnik V which is backed by the Russian Direct Investment Fund and another developed by Siberia's Vector Institute, with final trials for the both yet to be completed.
Scientists have raised concerns about the speed at which Russia has worked, giving the regulatory go-ahead for its vaccines and launching mass vaccinations before full trials to test its safety and efficacy had been completed.
The Sputnik V vaccine is administered in two injections, with the second dose is expected to be given 21 days after the first.
Deputy Prime Minister Tatiana Golikova said on Friday that the vaccinated should avoid public places and reduce their intake of medicine and alcohol, which could suppress the immune system, within the first 42 days after the first jab.
Moscow closed down all public places including parks and cafes, with exception for delivery, in late March, with police patrolling the streets looking for whose violating the rules. Restrictions were eased from mid-June, however.
Russia as a whole reported 28,782 new infections on Saturday, its highest daily tally, pushing the national total to 2,431,731, the fourth-highest in the world.
In October, certain restrictions such as remote learning for some secondary school children and a 30% limit on the number of workers allowed in offices were introduced again.