Moscow has said it may miss its growth targets this year and global markets have been bruised by the impact of the virus.
A sharp drop in the price of oil, Russia's main export, has left Russia particularly vulnerable, with the rouble sinking to four-year lows against the dollar.
The Finance Ministry and the central bank have already pledged support to everything from the banking sector to the rouble and the state debt market, and attention is now focused on a key interest rate meeting set for March 20.
Mishustin said new support measures would include tax breaks for tourism companies and airlines, and that Russia would expand its preferential loans programme for businesses.
Andrei Belousov, his first deputy, said last week that Russia may miss its economic growth target this year, originally set at 2%, while economists have warned that the country's economy may turn negative amid low oil prices and slower business activity.
Russia has 63 confirmed coronavirus cases and is building a new hospital outside Moscow to prepare for a possible increase in numbers. That is in addition to a hospital that was recently converted to treat coronavirus patients only.
There have been no deaths from coronavirus in Russia so far, the authorities say.
Russia is already restricting passenger flights and has halted many trains to Europe. Mishustin said on Monday that Russia would close its border with Belarus as well.
Russia has recommended that higher educational institutions switch to distance learning from Monday, while the city of Moscow has made school attendance optional.
There have been some signs of panic buying. Shelves over the weekend in a number of Moscow shops were lacking toilet paper, washing powder and canned products as well as riсe and flour.