Officials familiar with the situation told the Post that the three non-commissioned officers allegedly broke a curfew during Trump’s Vietnam visit.
The service members had been working for the White House Communications Agency, a specialized military unit that helps provide top officials with secure communications, the Post said.
Pentagon spokesman Mark Wright confirmed the probe.
“We are aware of the incident and it is currently under investigation,” Wright told AFP, without providing additional details.
The investigation is the latest headache for US security detail accompanying top officials on overseas trips.
The Post said that four troops from the same White House team faced allegations around accompanying women, stemming from a trip to Panama in August with Vice President Mike Pence.
In another incident in 2012, Secret Service agents in Cartagena, Colombia were caught soliciting prostitutes.