Punjab police chief Javed Iqbal said a suspect identified as Usman was arrested at the site of the blast yesterday.
Acting on information provided by Usman, police conducted raids and arrested two more suspects, Iqbal told reporters on the sidelines of a function at a police training school here.
The arrested persons allegedly had links with a militant group but Iqbal refused to say whether they were members of the Punjabi Taliban.
The arrests had helped uncover the network behind yesterday's attack in Faisalabad, he said. Iqbal acknowledged that the attackers wanted to target the ISI office. The car bomb caused widespread devastation when it went off at a CNG station near the ISI office.
Several nearby buildings, including an office of the state-run Pakistan International Airlines, were damaged by the explosion.
The owner of the banned Tehrik-e-Taliban Pakistan claimed responsibility for the attack, saying it was carried out to avenge the killing of a former Lashker-e-Taiba commander who was shot dead by security forces in Faisalabad last year.