The local currency was quoted at 1,112.0 against the dollar at the end of onshore trade, compared with 1,111.3 at the end of the Seoul session on Friday.
Dealers said the won was trapped in a narrow range, with investors split over whether the better-than-expected US September unemployment rate was an aberration or a turning point for the country's growth.
"There is some dollar-selling from exporters, but also some unwinding of dollar-short positions and some dollar-long positions being established," a foreign bank dealer said, noting that these elements were offsetting each other and limiting the won's volatility.
South Korean officials told Reuters that the country's foreign-exchange authorities will not intervene to weaken the won despite slumping exports because a won depreciation could also undermine domestic demand.
Market participants said the comments may mean the won will be allowed to strengthen further, easing some worries that the authorities would block any attempts by the market to push the currency higher over coming weeks.
The won has risen by 3.6 percent against the dollar so far this year, although it touched a near one-year low of 1,109.6 in intraday trading on Friday.
The benchmark Korea Composite Stock Price Index ended down 0.7 percent at 1,981.89. Foreigners were net sellers of 58.4 billion won ($52.55 million) worth of local shares on Monday.
Local bonds weakened slightly on profit-taking, following the decline of US treasuries' on Friday after the strong US jobs report. December futures on three-year treasury bonds ended down 0.03 points at 106.35.