Mr Hun Sen's court complaint, filed on Monday, said Mr Rainsy had not only defamed the government but also "incited the public".
He asked for just 100 riel ($0.025) in compensation.
Mr Rainsy said that there was "no other explanation" for Kem Ley's murder.
Tens of thousands of Cambodians joined his funeral procession on 24 July.
Kem Ley was a prominent commentator in local media and was known for being unafraid to criticise politicians on both sides of Cambodia's polarised political landscape.
He was shot dead while drinking coffee at a local petrol station, days after commenting on an investigation into the business dealings of Mr Hun Sen and his family members.
Police said the alleged killer had confessed to shooting Kem Ley over an outstanding debt.
But Mr Rainsy, who currently resides in France to avoid arrest for an old defamation conviction, called it "state terrorism".
He compared it to previous killings of government critics in a Facebook post, saying "only the government had the means and the capabilities to conduct such brazen attacks, to arrange for their cover-up and to ensure a total impunity for the perpetrators and their mastermind".
Several politicians from the Cambodia National Rescue Party (CNRP), which Mr Rainsy leads, have been hit with lawsuits in recent months.
Mr Hun Sen has led Cambodia for more than 30 years, presiding over dramatic developments while ruling with what critics say is an iron fist.
He has recently enthusiastically taken to Facebook to project a softer image, but has been accused of buying fake likes to boost his popularity.
Cambodian Prime Minister Hun Sen has sued opposition leader Sam Rainsy for defamation for saying the government was behind the killing of a political analyst last month.