The flame was held in two special containers in a seat on a chartered Aeroflot flight from Athens that landed at the city's Vnukovo International Airport.
It was to be received by a guard of honor on the tarmac before a ceremony near the terminal building.
From there, the flame will be transported to Red Square in central Moscow in a bikers' convoy.
The flame was kindled in a traditional ceremony in Ancient Olympia last Sunday and toured Greece before arriving in the Russian capital for the longest torch relay in history, a 123-day, 56,000-kilometer marathon across nine time zones.
The domestic relay itself is to begin Monday, but on Sunday there will be a mini-relay within the Kremlin in the presence of President Vladimir Putin.