The 13, seven of whom appeared in a Phnom Penh court, are linked to a little-known group called the Khmer National Liberation Front (KNLF), based in Denmark, said Phnom Penh Municipal Court judge Seng Neang.
He sentenced all of the 13, including six in absentia, to jail terms of between five and nine years for planning to topple Hun Sen's government.
The seven men, dressed in pink prison uniforms, shouted in protest after they were sentenced, saying the court had no evidence or witnesses to prove their guilt.
"I want the international community to look at Cambodia," one of the men said. "There is no justice for me, where are the evidence and witnesses?"
Seng Neang said the KNLF had set up an armed force based in neighbouring Thailand and had distributed anti-government leaflets between 2009 and 2011.
The group planned to plant bombs, Seng Neang told the court without giving details of any evidence.
Hun Sen and his Cambodian People's Party (CPP) have ruled since the 1980s, when he rose to power as part of a government backed by neighbouring Vietnam that ousted the 1975-79 Khmer Rouge regime.
He has earned a reputation as a tough leader who brooks no dissent. Critics say he has intimidated opponents and rigged elections for years while human rights groups criticise his government's record on rights.
"This was all about using a tiny exile group from abroad to try and smear the broader movement of opposition to the CPP and Hun Sen - and these long prison sentences are indicative of that," Phil Robertson, Asia deputy director at Human Rights Watch, told Reuters in an e-mail.
Hun Sen and his government deny violating human rights and say they have brought peace, stability and relative prosperity to one of Asia's poorest countries after decades of war and instability.
Ang Chanrith, director of the Minority Rights Organisation (MIRO) rights group, questioned the assertion that the KNLF group promoted violence.
"If the Danish government allows the KNLF to operate on its territory, the Cambodian courts should not assume it has unlawful motives," he said.