Russia lifted many of its lockdown restrictions in June and many shops, businesses and public transport in the capital of more than 12.5 million people are operating largely as normal.
But on Friday Mayor Sergei Sobyanin recommended that the heads of all companies in the city switch as many of their staff as possible to working from home from Monday.
TsUM, Moscow's flagship luxury goods department store, was fined 1 million roubles ($13,000) for failing to make its visitors wear masks, the city's coronavirus taskforce said.
It said raids to check for mandatory mask-wearing in shops were continuing and that more than 15,000 fines had been issued.
Sobyanin advised anyone with chronic health problems or those older than 65 to stay at home except in urgent circumstances. Any pension-age working Muscovites should work from home or take holiday, he said.
The national coronavirus taskforce said 108 people had died across Russia in the last 24 hours, pushing the official coronavirus death toll to 20,056.