"The authorities are investigating and looking for him," Chhum Sucheat told Reuters. He identified the man as Vichea Som but declined to give further details.
News of the plot comes a day after a senior U.S. official responsible for human rights urged Cambodia's political rivals to return to negotiations amid a "deteriorating situation".
In the video, the man the ministry identified as Vichea Som is dressed in a business suit and tie with a camouflage background visible in the footage.
He did not identify himself but accused Hun Sen's government and his ruling Cambodian People's Party of being behind big land grabs in one of Southeast Asia's poorest countries. He also accused the government of high-profile killings and human rights abuses.
"In the near future, please all forces be ready against the dictatorial regime," the man said.
He did not specifically call for a coup or threaten to organize a coup in the video clip.
It was not clear where he was speaking from but he said he belonged to a "unit" based in southwestern Cambodia.
The Facebook page bearing the name Vichea Som showed the same man. He did not immediately respond to a request for comment sent via Facebook.
Hun Sen has ruled with an iron fist for more than 30 years, defeating all challenges to his authority, but he faces a young electorate which appears increasingly hungry for change.
In recent moths, tension has been rising between Hun Sen and an opposition hoping to challenge his grip in local elections next year and a general election in 2018.
Several members of the opposition and activists have been jailed as part of what they say is a government crackdown to silence critics ahead of the elections.
On July 10, Kem Ley, a prominent activist and frequent critic of Hun Sen, was murdered in the capital Phnom Penh.
A suspect has been arrested and police said they believed Kem Ley was killed because of a debt. Activists believe his murder was political.
The United States has called for a credible investigation. The European Union and United Nations have expressed concern about the political tension.
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