"Malik Ishaq, along with 13 other sectarian militants, including two of his sons, were killed in the early hours of Wednesday morning," Punjab Home Minister Shuja Khanzada told AFP.
Ishaq, arrested on July 25, was being moved between prisons when his followers attacked the convoy in the Muzaffargarh district of Punjab to set him free, a senior police official said.
"The police retaliated and in the encounter, Ishaq, his two sons and 11 others were killed, while six policemen were injured," he added.
Mushtaq Rasoor, chief doctor at the Muzaffargarh District Hospital, said he had received 14 dead bodies.
Last year, the US State Department declared Ishaq a “specially designated global terrorist.”
Founded in 1996, the Lashkar-e-Jhangvi terror group is responsible for killing hundreds of Shia Muslims in Pakistan, who say the government must take decisive actions against the forces involved in the targeted killings.
The Shias also accuse Islamabad of failing to provide proper security for the Muslim community.
Shia Muslims make up about a third of Pakistan's population of over 180 million.