The online newspaper VnExpress said the new regulation was part of the revised Penal Code that an overwhelmingly majority passed in the National Assembly today.
Under the revision, which takes effect July 1, 2016, the country also will abolish the death penalty for seven crimes: surrendering to the enemy, opposing order, destruction of projects of national security importance, robbery, drug possession, drug appropriation, and the production and trade of fake food.
The ruling Communist Party has made fighting corruption one of its top priorities.
However, some lawmakers had voiced opposition to the changes when they were debated in the assembly in June, arguing that they would weaken the fight against corruption.
"This would create a loophole for corrupt officials to use money to trade for their life," state media quoted deputy Do Ngoc Nien as saying at the time.
International human rights groups and some Western countries have been urging Vietnam to abolish its death penalty.