It is believed that the move had the backing of the presidency.
The bill was reportedly withdrawn because Babar did not get it approved by a special committee of the ruling Pakistan People's Party headed by Law Minister Farook H Naek. This committee approves all private members' bills.
The bill could be submitted for consideration in the next session of the Senate, media reports said.
Sources said opposition from the powerful security establishment could also have contributed to Babar's decision to withdraw the bill.
The proposed ISI (Functions, Powers and Regulation) Act of 2012 said the spy agency should be answerable to the parliament and the prime minister.
It recommended internal accountability within the agency and a better discipline system to end enforced disappearances and victimisation of political parties.
In 2008, former premier Yousuf Raza Gilani called off an attempt to place the ISI under the control of the interior ministry after the powerful army objected to the move.