Vietcombank sold the greenback at VND26,388, up just 0.004% from the weekend. The currency dropped 0.03% to around VND26,673 on the black market.
The State Bank of Vietnam raised its reference rate by 0.004% to VND25,132.
Globally, the dollar fell on Monday as investors unnerved by U.S. President Donald Trump's latest tariff threats against Europe over Greenland piled into the safe-haven yen and Swiss franc, in a broad risk-averse move across markets, Reuters reported.
The euro gained 0.21% to trade at $1.1623, reversing earlier losses that sent it a seven-week, while the British pound recovered 0.11% from a one-month trough to $1.3390.
The greenback slid 0.36% against the safe-haven Swiss franc to 0.7993, and was down 0.24% to 157.74 yen. The dollar index eased slightly to 99.18.
"Typically you would think tariffs being threatened would lead to a weaker euro, but as we've seen last year as well, when the Liberation Day tariffs were getting put in place, the impact in FX markets actually has been more towards dollar weakness every time there is heightened policy uncertainty emanating from the U.S.," said Khoon Goh, head of Asia research at ANZ.