The news comes less than a week after the ruling Pakistan Muslim League-Nawaz (PML-N), founded by Sharif, finished its five-year term, handing power to a technocratic caretaker government until elections on July 25.
The National Accountability Bureau's (NAB) decision, involving an unidentified terminal is one of the world's fastest growing LNG markets, is part of a sweeping new initiative targeting senior politicians across the South Asian nation.
The national exchequer had suffered a loss of billions of rupees, the NAB said in ordering the inquiry against Abbasi, Sharif and others for granting a 15-year LNG terminal contract "to a company of their liking, in violation of rules and by misuse of their powers".
It did not say which of Pakistan's two completed terminal projects was referred to. Several more are in the pipeline.
Abbasi, who ended PML-N's term as premier, told Reuters he was unaware of any NAB inquiry, and nobody had contacted him.
As petroleum minister when Sharif was premier, Abbasi masterminded Pakistan's push to embrace LNG after PML-N swept to power in a 2013 election.
He added, "I welcome any inquiry by NAB or any other agency into the affairs of the ministry and I am available to cooperate with any such inquiry."
Text messages and telephone calls to the spokesman of Sharif, who has accused the judiciary of a witch hunt against his party, received no response.
The corruption agency also approved an inquiry against Sharif's brother Shehbaz, formerly the chief minister of the vast eastern province of Punjab, who is seen as the favourite to fight the next election as PML-N's prime ministerial candidate.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)