Russia seized three Ukrainian naval ships on Sunday after opening fire on them and wounding several sailors, a move that risks igniting a dangerous new crisis between the two countries.
At 0716 GMT, the rouble was 0.6 percent weaker against the dollar at 66.57, a level last seen on Nov. 15.
Versus the euro, the rouble shed 0.7 percent of its value to 75.60.
"The escalation of conflict between Russia and Ukraine... clearly creates negative background for the rouble in the short term," said Dmitry Dolgin, chief economist at ING Bank in Moscow.
"It is quite likely that we will see a negative adjustment in Russian assets, such as the rouble and OFZ bonds, that emerged late last week even despite today's support from tax payments," said analysts at Rosbank, a subsidiary of Societe Generale.
The rouble proved to be resilient to a rapid drop in oil prices last week as it gained support from month-end tax payments that usually prompt export-focused companies to convert dollar revenues to meet local liabilities.
Brent crude oil, a global benchmark for Russia's main export, was up 2.2 percent at $60.06 a barrel after last week's drop to $58.41.
A trade war between the world's two biggest economies and oil consumers, the United States and China, has weighed on the energy market this month.
Oil prices are in focus again ahead of the G20 meeting in Argentina this week, where U.S. President Donald Trump and his Chinese counterpart Xi Jinping are set to meet.
Russian stock indexes fell. The dollar-denominated RTS index was down 1.6 percent at 1,095.7 points, while the rouble-based MOEX Russian index was 1.3 percent lower at 2,313.6 points.