Two metal balls were discovered in northwestern Yen Bai province on January 2, army spokesman Lieutenant General Vo Van Tuan told AFP.
Later a larger ball weighing some 45 kilograms landed in a maize field in neighbouring Tuyen Quang province, he said.
"We are still identifying where they came from," he said, adding the army had determined they did not contain explosives or hazardous material.
The metal balls fell from the sky, he said, scaring local residents.
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Witnesses told state-run media that they heard what sounded like thunder before the balls plunged to the earth.
The Ministry of Defence has pledged to release the findings of the probe.
Thanh Nien newspaper said that the initial investigation suggested the objects could have been made in Russia and come from missiles or spaceships.
Nguyen Khoa Son, a professor from the Vietnamese Space Science and Technology Program, told the VietnamNet news site that the balls might be the result of a failed satellite launch.
In November, three mysterious objects also fell from the sky onto Spain's southeast.
According to NASA, more than 500,000 pieces of debris are currently orbiting Earth, and bits of space junk plummet to the planet every year.