The men, aged 54 and 52, were killed immediately on Saturday as they tried to disassemble a US-made 105-millimetre shell that they found in a local field, the Thanh Nien newspaper reported.
The injured 46-year-old man needed part of his leg amputated following the explosion in central Quang Ngai province, and he remains in a critical condition, the paper said.
A study in 2009 showed that leftover ordnance had killed 10,529 people and wounded more than 12,000 in six heavily-contaminated provinces of central Vietnam since the conflict betweeen US and Vietnamese forces ended in 1975.
The government last year approved a plan to clear about 1.3 million hectares, or 20 per cent of the nation's land contaminated by unexploded munitions.
Vietnamese officials estimated they need more than 34 trillion dong (1.62 billion dollars) for the cleanup.
