At 0716 GMT, the rouble was 0.5pc weaker against the dollar at 63.79 and also 0.5pc weaker against the euro at 69.10.
"Negative sentiment on the local Russian market could persist in the future over concerns about the impact of the coronavirus on the global economy, which contributes to a decrease in appetite for risky assets, including emerging market currencies and energy," said Bogdan Zvarich, chief analyst at Promsvyazbank.
The rouble is getting some support from Russia's month-end tax period, which prompts export-focused companies to convert their foreign currency revenues to meet local liabilities.
The rouble could also benefit from OFZ treasury bond auctions held by the finance ministry on Wednesday.
Demand for these bonds, which serves as a gauge of global market sentiment toward Russian assets, has been strong in recent months.
Russian stock indexes were trading lower.
The dollar-denominated RTS index was down 1pc to 1,528.1 points, and the rouble-based MOEX Russian index was 0.5pc lower at 3,094.3 points.
Prices for Brent crude oil, a global benchmark for Russia's main export, was were down 1pc at $57.09 a barrel by 0703 GMT.