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The currency was quoted at 1,020.1 per dollar at the end of onshore trade, the weakest close since June 5 and down 0.2 percent from Friday's 1,017.8.
The Korea Composite Stock Price Index (KOSPI) finished up 0.1 percent at 1,993.59 points, after Friday's 1 percent decline, which was the worst daily percentage fall in seven weeks.
Market bellwether Samsung Electronics Co Ltd edged up 0.5 percent, and memory-chip maker SK Hynix Inc advanced 2.8 percent.