The local currency was up 0.32 percent at 8.6865 at 0649 GMT compared with Friday's closing level of 8.7140.
"It's a US holiday today and that's kind of reflected in the Far East trading which has been very narrow and very quiet and I would expect us to be pretty quiet today because of that," RMB trader Jim Bryson said.
"A quiet day for the euro will probably equal a quiet day for the rand and we'll probably trade within 8.65/75.
"There's no real (domestic) news at the moment."
Some US markets, including the bond market, will be closed in observance of the Veterans Day holiday on Monday, although the equity market will be open.
With most of the strikes that have plagued the mining sector in particular since August now more or less resolved, the next local focus for markets should be the ruling ANC's conference in December, widely expected to retain President Jacob Zuma as party leader.
"Unless there's some real surprises from that it shouldn't really be too much of a factor for us," Bryson added.
Government bonds also got off to a quiet start on Monday, with the yields on the benchmark 14-year bond and the three-year paper each shedding a basis point to 5.45 percent and 7.605 percent respectively.