Mr Quang died in a military hospital in Hanoi from a "serious illness, despite efforts by domestic and global doctors and professors", Vietnam Television reported.
The official Vietnam News Agency says Quang died at the 108 Military Hospital in Hanoi on Friday due to a serious illness.
Rumours of his illness had circulated on social media for months, and there was no significant reaction in Vietnam's benchmark index.VNI.
In Vietnam the role of president is largely ceremonial.
While President Tran Dai Quang's role was mostly ceremonial, he was the government's most public face at high-profile events, including at the APEC meeting in Vietnam's Danang in November a year ago where he hosted world leaders including US President Donald Trump and China's President Xi Jinping.
At one of his last appearances was during a visit by Indonesian President Joko Widodo to Hanoi on September 11.
As president, Quang was reputed to be tough on dissent, with his government overseeing a crackdown on rights groups.
The state-run online newspaper VnExpress quoted a former health minister and the head of a national committee in charge of leaders' health, Nguyen Quoc Trieu, as saying that Quang had contracted a rare and toxic virus since July previous year and had travelled to Japan six times for treatment.
Adam Sitkoff, executive director of the American Chamber of Commerce in Hanoi, said: "He was the first Vietnam president to meet with us, speak at a US-Vietnam business summit".
Quang was a member the Politburo, the decision-making body of the Communist Party of Vietnam.
Born in northern Ninh Binh province, Quang attended a police college and rose through the ranks at the powerful Ministry of Public Security before being appointed minister in 2011. More than 40 people were jailed this year and some 100 have been behind bars as of April 2018, according to Amnesty International.
The National Assembly is scheduled to convene a session next month and expected to elect a new president.