Mukherjee will visit both Hanoi and Ho Chi Minh City.
It was not immediately clear how the tourists – reported to be two women aged 19 and 25, and a man – had died.
Local news reports said police believed the visitors might have slipped while exploring the Datanla waterfalls. A local man who had taken them to the falls has been questioned by police.
Their bodies were found downstream from the falls, in Lam Dong province, which are popular with Western visitors.
Emergency workers had climbed down a steep slope to recover the bodies, which were found wearing life jackets, the local reports said.
Deputy director of the tourist company which manages the falls, Vo Anh Tan, said visitors usually started at the top of the tiered waterfalls.
The Foreign Office said: “We are providing support to the families of three British nationals following their deaths near Da Lat, Vietnam.
“Our sympathies are with their families and friends at this difficult time. We are in close contact with local authorities in Vietnam on their behalf.”
Da Lat is the capital of Lam Dong province, in the country’s Central Highland