Sailors will also visit a center for victims of Agent Orange, a defoliant used by the US military during the war, according to a report in The New York Times.
Vietnamese leaders agreed to the four-day port call during President Donald J. Trump's visit to the country previous year.
"We've seen several, so yes, we've seen Chinese ships", Rear Admiral John Fuller, Commander, Carrier Strike Group 1, told reporters in Danang.
"Through hard work, mutual respect, and by continuing to address the past while we work towards a better future, we have gone from former enemies to close partners", he continued. The Carl Vinson carries over 5,000 sailors, which is the largest contingent of American soldiers to land in Vietnam since USA troops withdrew in 1975.
In recent years, the United States and Vietnam have worked to improve relations that were normalized in 1995. It will anchor just off Danang, where US Marines landed 53 years ago this month - the first direct involvement by American combat troops in the war. The vessel can carry up to 90 on-deck aircraft.
In July 2016, an worldwide court ruled that the so-called "nine-dash line"-a demarcation line China uses to lay claim to parts of the South China Sea-is inconsistent with global laws governing maritime resources". Fuller's father served in Vietnam.
Some Chinese commentators have used the USS Carl Vinson's presence in the region as justification to demand a rise in Chinese military build-up in the South China Sea.
Sailors are expected to participate in cultural and professional exchanges during community service projects and receptions.
The US has always said it does not take sides in the South China Sea dispute, but the US Navy has consistently run so-called "freedom of navigation" operations through disputed waters, a clear challenge to China's territorial ambitions.
Separately from this week's mission, USA officials have said American warships would continue sailing without prior notice close to the China-occupied islands and atolls, an aggressive way of signaling to Beijing that it does not recognize its sovereignty over those areas.
"It's a message to Vietnam, about how much we care about that relationship; it's a message to China, about what they're doing in the region; but it's also a broader message to everyone in the Pacific region, that the United States is here and we're here to stay", Kirby said.
Vietnam Foreign Ministry spokeswoman Le Thi Thu Hang said the visit will "continue to promote bilateral relations within the framework of the two countries' comprehensive partnership and contribute to maintaining peace, stability, security, cooperation and development in the region".
The Vietnam War - which Vietnam calls the American War - was protracted and bloody.
China claims sovereignty over nearly all of the South China Sea, where more than $5 trillion of goods are shipped each year through some of the world's busiest waterways.