Ahead of the four-day visit, Merkel, who will be accompanied by top business leaders eyeing up investment opportunities, stressed the need to boost ties between the two fast-growing Asian nations and Europe's top economy.
"Vietnam is an emerging country in Asia, has enjoyed fast-paced economic growth in recent years and is increasingly becoming a competitor for large nations like China," Merkel said in her regular podcast over the weekend.
A senior government source in Berlin said Merkel would push for the conclusion of a free-trade accord between the EU and Vietnam. Germany "is a very strong supporter" of such a deal, the source said.
Merkel noted that Germany and Vietnam have long enjoyed close relations, stemming from the days before the fall of the Berlin Wall, when young Vietnamese came to study or work in the former communist east.
After Vietnam, Merkel heads to Mongolia for the first visit by a German leader since the two countries established diplomatic relations, with media speculating that deals worth $2 billion could be inked.
"Mongolia is a country very rich in raw materials and we have a very, very good chance to improve our cooperation in this field," Merkel said.
German firms have said they are keen to conclude agreements on rare earths in Mongolia.
Rare earth elements are a collection of 17 substances that are not in fact rare but which are rarely found in quantities that make mining economically advantageous.
They are nonetheless critical for the manufacturing of items like iPods, low-emission cars, wind turbines and missiles.
At a crunch meeting with French President Nicolas Sarkozy late on Sunday, Merkel pledged to do what what necessary to recapitalize European banks as the two leaders vowed to come up with a "long-lasting" solution to the euro crisis.
Paris and Berlin would present a blueprint for exiting the debt drama by the end of the month, Merkel and Sarkozy said.
Merkel was due to leave mid-afternoon from Berlin, arriving in Hanoi late in the evening, local time.