At 0748 GMT, the rouble was 0.2pc stronger against the dollar at 61.81 and had gained 0.2pc to trade at 68.27 versus the euro.
China stepped up measures to contain the new coronavirus, which has killed 25 people and infected more than 800 as of Friday morning, with public transport suspensions in 10 cities and temples shutting, just as the country begins to celebrate the Lunar New Year.
The World Health Organisation (WHO) on Thursday declared an emergency for China but stopped short of declaring the epidemic a global emergency.
This soothed markets, VTB Capital analysts said in a note.
The rouble was supported by month-end tax payments that usually prompt export-focused companies to convert their foreign currency revenues, as well as income tax which is due at the start of next week.
But Russia's daily foreign exchange purchases, which the finance ministry said it would double in January, have exerted pressure on the currency.
Brent crude oil, a global benchmark for Russia's main export, was up 0.6pc at $62.4 a barrel, after falling to a seven-month low on Thursday.
Russian stock indexes were up on Friday and seeking to resume their general upward trajectory since early December, after falling sharply in the previous two trading sessions.
"Virus-related fears sent global equity markets into risk-off mode, but the weakness in Russian stocks was exacerbated by a sharp sell-off in crude prices," Aton Research analysts said in a note.
The dollar-denominated RTS index was up 0.9pc to 1,610.7 points. The rouble-based MOEX Russian index was 0.6pc higher at 3,159.9 points.