Abbasi was arrested by a 12-member NAB team when he was on his way to attend a press conference, accompanied by PML-N leader Ahsan Iqbal, Dawn reported.
Abbasi initially resisted the arrest but eventually gave up, the report said.
The case pertains to a case of LNG import contract when Abbasi was the minister of petroleum and natural resources.
He is expected to be presented before an accountability court for physical remand on Friday.
Abbasi, who succeeded former PM Nawaz Sharif after he was forced to quit following corruption allegations in 2017, served as Pak premier for less than a year. Sharif was ultimately convicted and jailed.
Shehbaz Sharif, the Leader of the Opposition in the National Assembly and former Punjab province Chief Minister, condemned the arrest.
"We strongly protest Shahid Khaqan Abbasi's arrest. The institution of NAB has become Imran Khan's puppet. Our spirits cannot be wavered by such cheap tactics," he said.
TheDawn report said that the NAB had summoned Abbasi in the LNG case but he did not appear before the bureau. The former premier had only answered 20 out of the 75 questions he has been asked by the probe team.
"You are requested to appear on 18-07-2019 at 10 am at NAB Islamabad before Investigation Officer Malik Zubair Ahmed, deputy director, for discussion and recording your statement being minister of petroleum and natural resources on LNG terminal," said the NAB notice that was served to Abbasi.
"You are advised that failing with this notice may entail penal consequences as provided in serial 2 of the schedule of the National Accountability Ordinance 1999," the notice said.
In April, the government had imposed a travel ban on Abbasi, former Finance Minister Miftah Ismail, and five other persons in the same case.