Vietcombank sold the greenback at VND26,451, down 0.008% from the weekend. The currency traded at around VND26,650 on the black market.
The State Bank of Vietnam lowered its rate by 0.008% to VND25,192.
Globally, the dollar eased as investors braced for a possible shutdown of the U.S. government, which would in turn delay publication of the September payrolls report and a raft of other key data, Reuters reported.
A protracted closure could leave the Federal Reserve flying blind on the economy when it meets on October 29.
"If the shutdown lasts beyond the Fed meeting, the Fed will rely on private data for its policy decisions," analysts at BofA wrote in a note. "On the margin, we think this may lower the likelihood of an October cut, but only marginally."
The dollar index slipped back 0.2% to 97.952, having benefited last week from the batch of better economic news. The euro nudged up to $1.1726, but was still in the lower half of its recent $1.1646 to $1.1918 range.
The dollar eased 0.4% to 148.92 yen, after rallying just over 1% last week and away from the September low around 145.50.