The spot rupee ended at 153.97/154.05, compared with Friday's close of 153.95/154.05.
Sri Lanka's stock, bonds, and foreign exchange markets were closed on Monday for a bank holiday.
"Today there was heavy demand (for dollars) from some foreign banks for a payment. There was heavy remittance flow too, but rupee ended weaker due to heavy demand," said a currency dealer.
Sri Lanka aims to raise $500 million this month via development bonds (SLDB), the central bank said last week, as the government faces unprecedented debt repayment this year.
President Maithripala Sirisenea's administration must repay an estimated 1.97 trillion rupees ($12.85 billion) in 2018 - a record high - including $2.9 billion of foreign loans, and a total of $5.36 billion of interest.
The currency fell 2.5 percent last year and 3.9 percent in 2016.
The central bank, while announcing its key economic policies for the year on Jan 3, said it has allowed more flexibility in determining the exchange rate based on market conditions.
It has also said intervention policies will be adopted consistent with a flexible exchange rate regime and supportive of improving foreign exchange market functionality, and maintaining a competitive exchange rate will be an important objective.