The petition also sought to commence a criminal proceeding against Sharif for his statement on the 2008 Mumbai terror attacks.
Advocate Babar Awan, a leader of the Pakistan Tehreek-i-Insaf (PTI) has filed the petition on the behest of a local lawyer.
According to the report, the petition stated that Sharif on May 3, during his appearance before the accountability court, had threatened to reveal some national secrets.
The petition requested the court to direct the Federal Investigation Agency (FIA) to initiate legal proceedings against Sharif.
Justice Aamer Farooq sought reply from the director general of the FIA, chairmen Pakistan Electronic Media Regulatory Authority (Pemra) and Pakistan Telecommunication Authority (PTA) with respect to the filed petition.
He questioned if the court could impose a ban on someone delivering speeches.
Last week, during an interview with the Dawn, Sharif had stated that "Militant organisations are active. Call them non-state actors, should we allow them to cross the border and kill 150 people in Mumbai? Explain it to me. Why can't we complete the trial?"
"We have isolated ourselves. Despite giving sacrifices, our narrative is not being accepted. Afghanistan's narrative is being accepted, but ours is not. We must look into it," he added.
His remarks were immediately picked up by Indian media, which termed the former prime minister's statement as a confession of Pakistan's role in the Mumbai attacks that left 166 people dead. (ANI)