Its developers say it is 95% effective and causes no major side effects, but it is still undergoing mass testing.
The vaccine was made avaialbale via 70 clinics on Saturday.
Thousands of people have already registered to get the first of two jabs over the weekend.
President Vladimir Putin has ordered a nationwide voluntary vaccination programme to begin next week.
He said Russia will have produced 2 million vaccine doses within the next few days.
“Over the first five hours, 5,000 people signed up for the jab - teachers, doctors, social workers, those who are today risking their health and lives the most,” Mayor Sergei Sobyanin wrote on his personal website on Friday.
Russia has already vaccinated more than 100,000 high-risk people, Health Minister Mikhail Murashko said earlier this week during a separate presentation to the United Nations about Sputnik V.
Among the first people signing up to the Moscow roll-out, Nadezhda Ragulina, an administrator at a Moscow clinic, said she wanted the vaccine as she had witnessed many COVID-19 patients.
“This is my decision... Some people close to me also have had an experience (of COVID-19). That’s why I want to protect myself, my relatives, to obtain the immunity,” she told Rossiya-24 state TV channel.
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.