The decision of the National Accountability Bureau (NAB) came just days after the Sharif party completed its five years term, with elections due on July 25.
Sharif, Abbasi and their staff have been accused of awarding the Liquid Natural Gas (LNG) terminal contract based on nepotism, causing billions of rupees of losses.
The NAB initially opened the investigation in 2015, closed it in December 2016 and reopened it again last Wednesday.
Abbasiwas minister for petroleum and natural resources when the contract was awarded in 2013.He told Reuters he was welcoming an inquiry and is available for cooperation.
Corruption in Pakistan is rampant and the country is listed as one of the most corrupt in the world. Transparency Internationals 2017 Corruption Perception Index ranks it 116 out of 180 countries.
