The office of Swiss Attorney General Michael Lauber said the request pertained to possible violations of Swiss laws related to bribery of foreign officials, misconduct in public office, money laundering and criminal mismanagement at 1MDB.
Earlier this week, Malaysia's attorney general cleared Prime Minister Najib Razak of any criminal offences or corruption, declaring that $681 million deposited into his personal bank account was a gift from Saudi Arabia's Royal family.
1MDB, whose advisory board is chaired by Najib, was being examined by Malaysian authorities investigating accusations of financial mismanagement and graft. The fund has been dogged by controversy over its $11 billion debt and alleged financial mismanagement.
The Swiss statement said Lauber's investigation had already "revealed serious indications that funds have been misappropriated from Malaysian state companies."
Those funds "would have been earmarked for investment in economic and social development projects in Malaysia," the Swiss official said.
The Swiss prosecutor said the misappropriated amount was suspected to be around $4 billion. He said a small portion of the money had been transferred to accounts held in Switzerland by former Malaysian public officials and current and former public officials from the United Arab Emirates.
The statement said the prosecutor wanted legal assistance from Malaysian companies involved to try to find out whether "losses on this scale have been sustained."
The Swiss Attorney General's office opened criminal proceedings last August against two former 1MDB officials as well as "persons unknown." The statement on Friday said Lauber had discussed the case with his Malaysian counterpart at a meeting in Zurich in September.
Sources familiar with the September discussion between the two law enforcement officials said that the Malaysian official strongly urged Lauber to abandon his 1MDB-related investigation.
Malaysia's anti-graft agency said on Wednesday it will seek a review of a decision by the attorney-general to clear Najib.
1MDB is also under investigation by law enforcement agencies in Hong Kong and the United States, media and other sources have said.