The move comes as a nationwide protest movement over poor services, economic woes and official corruption enters its fourth week with demonstrators hoping to expel an elite they say has ruled the country like a cartel for decades.
Financial prosecutor Ali Ibrahim has launched probes into customs authority chief Badri al-Daher over suspected "waste of public funds", NNA reported.
It said he had ordered an inquiry into "all the ministers of successive governments since 1990".
Protesters have been demanding an overhaul of the political elite, which has hardly changed since the end of the country's devastating 1975-1990 civil war.
The prosecutor's decision came after lawyers brought a case against the officials in question over alleged misappropriation or use of public funds for personal purposes, along with "abuses of power which caused significant damage to Lebanese citizens", the agency said.
Authorities have proposed similar probes in recent days to show they are fighting corruption, but that has done little to calm public anger.
On Thursday, the financial prosecutor questioned former premier Fouad Siniora for three hours over $11 billion allegedly spent during his period in office from 2006 to 2008, the NNA said.
Siniora has in the past denied all accusations of misappropriation of public funds.
On Wednesday, the financial prosecutor filed a lawsuit against a senior Beirut airport official over alleged money laundering and bribery, NNA reported.
Last month, another prosecutor pressed charges against former prime minister Najib Mikati over allegations he wrongly received millions of dollars in subsidised housing loans, charges he denies.
Lebanon is ranked 138th out of 180 countries in Transparency International's 2018 corruption perceptions index, with key sectarian leaders accused of running demi-fiefdoms.
President Michel Aoun, who has pledged various reforms to combat corruption, gave assurances Wednesday that the next government would be made up of ministers free of any suspicion of corruption.
Prime Minister Saad Hariri resigned on October 29 under pressure from the street, but his government has stayed on in a caretaker capacity and leaders are continuing to haggle over the make-up of the next one.
Follow us on Twitter and Instagram to stay connected
