At 0723 GMT, the rouble was 0.3pc weaker against the dollar at 62.24 after hitting its weakest level since Jan. 6 of 62.36.
Versus the euro, the rouble shed 0.3pc to 68.70.
Crude prices fell more than 2pc to multi-month lows on Monday as the rising number of cases of the new coronavirus in China and city lockdowns there deepened concerns over oil demand.
Brent crude oil, a global benchmark for Russia's main export, fell 2.2pc to $59.34 a barrel, down from levels of around $66 per barrel seen a week ago.
The rouble is no longer the best performing currency against the dollar in the year-to-date terms as it used to be in early 2020, having dropped to the 9th place in the ranking even though market concerns about the coronavirus seem to be exaggerated and are likely to be short-lived, the rouble is likely to move towards the middle of the 62-63 range against the dollar in the short term, Promsvyazbank analysts said in a note.
On the flip side, the rouble's losses are likely to be limited by month-end tax payments that usually prompt export-focused companies to convert part of their foreign currency revenues to meet local liabilities.
Russian stock indexes were down. The dollar-denominated RTS index shed 1.9pc to 1,569.0 points.
The rouble-based MOEX Russian index was 1.3pc lower at 3,105.8 points, heading away from an all-time high of 3,226.89 hit a week ago.