Trading volumes were also lower as employees at state-run banks started a two-day strike on Monday. Although dealing rooms were fully operational, employees dealing with retail customers - who account for around one-fifth of daily trading volumes - were absent.
Caution also prevailed ahead of a week full of key reports, including the January trade data sometime this week, and consumer price index and industrial production on Wednesday.
The weaker end to the rupee contrasts with most emerging Asian currencies, which crawled higher as regional shares gained mildly after a seemingly disappointing U.S. jobs report.
Globally, investors will be paying keen attention to Federal Reserve Chair Janet Yellen's testimony before the U.S. Congress on Tuesday and again on Thursday, which could provide clues about her stance on the U.S. central bank's winddown of its monetary stimulus.
"U.S. jobs data didn't change investors' views on tapering much, and in the absence of other crucial data, domestic factors will be watched closely for further rupee direction," said Pramod Patil, head of foreign exchange and fixed income trading at United Overseas Bank.
The partially convertible rupee closed at 62.43/44 per dollar compared with Friday's close of 62.2825/2925.
The rupee started stronger on Monday on hopes of dollar inflows following the strong demand at the telecom spectrum auction, but lack of large flows and demand from importers pushed the rupee down in the second half.
"The market is continuing to expect inflows in connection to positive response to telecom spectrum auction but dollar demand will also be strong. I expect USD/INR to be in the range of 62.10-62.70 for this week," Patil added.
India's benchmark BSE index also fell 0.2 percent, snapping a four-session winning streak, in part as foreign investors sold a net $39.88 million worth of Indian shares in the secondary market on Friday, extending their selling streak to a seventh day.
In the offshore non-deliverable forwards, the one-month contract was at 62.74, while the three-month was at 63.60.