The report by the parliament's Public Accounts Committee (PAC) marked the first time an official Malaysian probe has suggested misconduct or recommended action over the scandal swirling around Najib.
Najib, who founded the state investment fund 1Malaysia Development Berhad (1MDB) in 2009, has battled for months to fend off allegations that billions of dollars were looted from 1MDB in complex overseas financial transactions.
He and 1MDB have consistently denied wrongdoing.
"The PAC is of the opinion that the former CEO of 1MDB Shahrol Azral Ibrahim Halmi has to take responsibility for those restrictions and weaknesses," the 106-page report said.
"As such, enforcement agencies are asked to investigate Shahrol Azral Ibrahim Halmi and anyone else related."
Shahrol was 1MDB's CEO from 2009 to 2013.
The report did not make further recommendations on who should be investigated, nor did it allege misconduct by Najib.
Najib has faced a cascade of corruption allegations stemming from 1MDB's troubles and his own admitted acceptance of a mysterious USD 681 million overseas payment.
Authorities in Switzerland, the United States, Singapore, Hong Kong and elsewhere are investigating.
Critics have alleged debt-stricken 1MDB, set up to fuel Malaysian development projects, was bled dry in a vast campaign of fraud and embezzlement stretching from the Middle East to the Caymans.
The Wall Street Journal, which has detailed many of the money movements, also last year revealed the USD 681 million payment made to Najib's bank accounts in 2013.
It has said in subsequent reports that he may have received more than USD 1 billion.