Justice SC Gupte has also restrained the channels from publishing its content on their websites.
The vacation court was hearing an application filed by Khan claiming that the allegations in the shows were defamatory and sought to "dramatise and sensationalise" the case.
The programme was first aired on May 21 on a news channel and its content was submitted before the high court, on a CD.
Khan filed a suit against the defendants and also moved a notice of motion seeking a restraint order against the channels from repeating the controversial programme.
His counsels – Gaurav Joshi, Munaf Virjee, Manhar Saini, instructed by DSK Legal – argued that the programmes would influence and prejudice the outcome of the case.
Despite serving notice, no lawyer had appeared for the television channels.
Justice Gupte observed that "the interest of justice would be served if the plaintiff (Khan) was asked to renew his application on June 2 with a fresh notice to the defendants."
The court has posted the matter for hearing on June 2 for ad-interim relief.
Khan is facing prosecution in the 2002 case wherein he allegedly ran his SUV over a group of people sleeping on a pavement in suburban Bandra, leaving one dead and four injured.