Sam Rainsy now lives in exile due to what he says is a politically motivated defamation conviction.
The amended legislation bars political leaders with convictions from running for office.
It also allows the Supreme Court to dissolve political parties whose leaders have criminal convictions.
Mr Rainsy stepped down from the helm of his opposition Cambodia National Rescue Party (CNRP) this month ahead of the changes, saying he wanted to protect the party.
The CNRP is the sole opposition party in parliament and poses a threat to the ruling Cambodian People's Party (CPP) in elections scheduled for next year.
It mounted a strong challenge at the last election in 2013, winning 55 seats in parliament compared to the CPP's 68.
Mr Hun Sen has been in charge of the formerly war-torn but now rapidly developing country for more than 30 years.
Opposition lawmakers boycotted Monday's vote and the controversial amendments were passed unanimously by ruling party MPs. They will now move to the Senate, where passage is seen as a formality.
Human Rights Watch said the move marked the consolidation of absolute power in Mr Hun Sen's hands.
"Hun Sen's election strategy is clear: bulldoze what's left of Cambodia's democratic institutions by using laws like this one, while simultaneously intimidating civil society into silence with arbitrary arrests of human rights defenders and threats to de-register troublesome NGOs,'' the group's Asia director, Phil Robertson, said.
The CNRP said the amendments could be used to intimidate and "destroy" rival parties.
The government says the rules apply to all political parties and are not meant to target the CNRP.
Some analysts say that massive Chinese investment in Cambodia and a lack of clarity about the new US administration's foreign policy has emboldened the CPP to crack down on political opponents.
The US Embassy has said it is deeply concerned about the legal amendments.