At 0703 GMT, the rouble was 0.7pc weaker against the US dollar at 63.62 and had lost 0.6pc to trade at 69.16 versus the euro.
Authorities in China's Hubei province, where the virus is believed to have originated, said 242 people had died from the virus on Wednesday, the fastest rise in the daily count since the pathogen was identified in December.
"If the external background doesn't start improving, the rouble-dollar pair will once again head toward 64," said Alexei Antonov of Alor Brokerage.
Russian stock indexes were down.
The dollar-denominated RTS index was down 0.8pc at 1,545.1 points, while the rouble-based MOEX Russian index was 0.1pc lower at 3,120.5 points.
Prices for Brent crude oil, a global benchmark for Russia's main export, slipped nearly 0.2pc to $55.64 a barrel by 0658 GMT.