Vietcombank sold the greenback at VND26,242, up 0.07% from the weekend.
The currency gained 0.11% to VND26,320 on the black market.
Globally, the dollar firmed against major currencies on Monday, driven by safe-haven buying from investors fearing the Israel-Iran fighting could escalate into a broader regional conflict as they braced for a week packed with central bank meetings, Reuters reported.
The dollar rose 0.14% to 144.3 Japanese yen, while the euro was 0.14% lower at $1.1534.
In early Asia hours, the greenback was steady against the Swiss franc at 0.81, while an index that measures the dollar against six others was steady at 98.25.
"The dollar's role as a safe haven will surely be tested, and recent price action has been inconclusive," said Win Thin, global head of markets strategy at Brown Brothers Harriman.
"If the Fed delivers a dovish hold as we expect, the dollar is likely to resume weakening due to the worsening fundamental backdrop in the U.S."
The currency has lost over 9% in value this year as investors remain nervous over Trump's deadline on trade deals that come due in about three weeks, while agreements with major trade partners including the European Union and Japan are yet to be signed.