The stock market also edged lower to a near four-month low despite foreign investors buying the island nation's risky assets.
The rupee settled at 179.80/180.00, compared with Friday's close of 178.65/85, market sources said.
They said importers bought dollars, which were in short supply due to a holiday in the US, as they expect heavy demand when the market reopens on Wednesday after a public holiday.
The local currency had posted a weekly loss of 0.42 percent in the last week due to high dollar demand from importers and outflows from the stock market.
It has risen 1.6 percent so far this year as exporters converted dollars and foreign investors purchased government securities amid stabilising investor confidence in Sri Lanka after the country repaid a $1 billion sovereign bond in mid-January.
The bond market saw inflows of 3.3 billion rupees in the week ended Feb. 13, recording its fourth straight weekly inflow, the latest central bank data showed.
Worries over heavy debt repayment after a 51-day political crisis that resulted in a series of credit rating downgrades dented investor sentiment as the country is struggling to repay its foreign loans.
Sri Lanka will bring forward a plan to raise $2 billion through the bond market after a delay in a pledged loan from Bank of China, sources close to the deal said on Monday.
The rupee dropped 16 percent in 2018, and was one of the worst-performing currencies in Asia due to heavy foreign outflows.
The Colombo Stock Exchange index fell 0.2 percent to 5,897.33 on Monday, its lowest close since Oct. 26.
The benchmark index had fallen 0.92 percent last week, after losing 0.3 percent in the previous week. It declined about 1 percent in January.
The turnover was 530.6 million rupees, less than last year's daily average of 834 million rupees.
Foreign investors were net buyers of 146 million rupees worth of shares on Monday.
They have been net sellers of 5.1 billion rupees worth of stocks so far this year, and 18.6 billion rupees since the political crisis began on Oct. 26, 2018.