The People's Justice Party (PKR) alleged that a donation of 2.6 billion ringgit ($645 million; 629 million euros) and the movement of funds involving debt-stricken 1Malaysia Development Berhad (1MDB) are linked to an election campaign in 2013.
"The fact is that the alleged amount spent by Najib far exceeds the allowable amount for elections," Nurul Izzah, vice president of PKR and daughter of the party's jailed leader Anwar Ibrahim, told Reuters news agency.
"This is a clear-cut breach of the election law," she said.
The PKR said that the 2.6 billion ringgit donation is more than 26 times the amount allowed for election campaigns.
According to Malaysian electoral laws, campaigns for state-level assemblies are limited to 100,000 ringgit ($24,800), while those for federal parliament are capped at 200,000 ringgit ($49,000).
In early August, the Malaysian Anti-Corruption Commission said that the funds in question were donations from the Middle East.
However, critics have grown increasingly wary after Prime Minister Razak reshuffled his cabinet in July, sacking ministers who had criticized him.
The move also included replacing Attorney General Abdul Gani Patail, who was heading corruption investigations into the prime minister.
Razak has accused the opposition of attempting to oust him from power.
The lawsuit named 1MDD, the Election Commission and Adnan Mansour, secretary-general of the prime minister's United Malays National Organization, the majority party in the ruling National Front coalition.
According to Reuters, the lawsuit demands that the ruling coalition be de-registered and the 2013 vote be voided to pave the way for fresh elections.
ls/kms (Reuters, AP, dpa)