A statement said that the chief justice himself is monitoring the situation.
Punjab government also constituted a Joint Investigation Team (JIT) to probe the incident.
As per the initial investigation report issued by the police, Pakistan Rangers VIP Venue shift in-charge Naik Abdur Razzaq reported - at around 10:45 PM on April 14 - that a stray bullet hit the upper collar of the main gate of a house in H Block Model Town in Lahore.
According to the preliminary observations of the Crime Scene Unit (CSU), the first shot that hit the main gate of the house could be a stray bullet which was sacked from a distance and was on the final stage of its parabolic trajectory.
The TV channel reported that Chief Justice of Pakistan Mian Saqib Nisar has reached the residence of the Supreme Court judge. It added that a search operation has been conducted on the probable direction of the bullet trajectory.
On Sunday, the residence of Justice Ijaz ul Ahsan was sacked twice in 12 hours.
The JIT, which was formed on Sunday, would be headed by DIG Investigation Sultan Chaudhry to track the unknown suspects who targeted the residence, close to the house of Chief Minister Punjab Shehbaz Sharif, twice over the weekend.
Justice Ahsan was part of the five-member bench that heard the high-profile Panamagate case previous year that led to the disqualification of Nawaz Sharif, the then prime minister.
Chairman Pakistan Tehreek-e-Insaf Imran Khan, who started the legal proceedings against Nawaz Sharif and his family, said that the shooting incident may be a political motive to "pressurise" the judiciary. He had taken oath as the new chief justice of Lahore High Court (LHC) in November 2015.
Pakistan People's Party (PPP) chairman Bilawal Bhutto while condemning the firing incident has called for an independent inquiry and immediate arrest of culprit.