He told his teammates and coach during lunch that day and posted his decision on his Facebook page.
He said he had been honored to play for the national team for 12 years and contribute to Vietnamese football, and thanked fans for showering great love, encouragement and affection on him and his teammates all along.
He wished Vietnamese football the best for the future.
Head coach Park Hang-seo said he agreed to Duc's departure when they discussed it earlier.
"Duc said it's time he saved the position for younger players," Park said at a press conference in Hanoi Tuesday night.
He will continue to play for his club side Becamex Binh Duong.
Duc made his debut against Jamaica in Hanoi in 2007.
Since then he has been a key player for the team, regularly starting until recently.
He helped Vietnam advance to the semi-finals of the 2018 ASIAD and win the 2018 AFF Suzuki Cup, where he scored the only goal in the final match against Malaysia.
He also scored Vietnam's only goal when they beat Thailand in the 2019 King's Cup.