Meanwhile, police raided the apartment of Khan's close aide Shahbaz Gill overnight in the Pakistan capital, and took him away in handcuffs for interrogation.
Tuesday's developments came two days after authorities filed terrorism charges against Khan, escalating political tensions in the country.
In a speech at a rally on Saturday, Khan vowed to sue police officers and a female judge, Zeba Chaudhry, and alleged that Gill had been tortured after his initial arrest earlier this month.
Khan, who came into power in 2018 and was ousted in April in a no-confidence vote in Parliament, could be disqualified for life from politics if convicted of insulting Chaudhry.
The terrorism charge against him could carry anything from several months to 14 years in prison, the equivalent of a life sentence.
Gill has been charged with treason for his recent anti-army remarks during a show on the private ARY TV in which he urged soldiers and officers to disobey "illegal" orders from military leaders.
The treason charge against Gill carries the death penalty under a sedition act that stems from a British colonial-era law. ARY TV remains off-air in Pakistan following that broadcast.
Since his ouster, Khan has alleged - without evidence - that Pakistan's powerful military took part in a US plot to oust him. Washington, the Pakistan military and the government of Khan's successor Shahbaz Sharif have all denied the allegation.
The latest trouble for Khan started at Saturday's rally when he criticised Chaudhry, saying, "You also get ready for it, we will also take action against you. All of you must be ashamed."
Sharif's government is unhappy with Khan over his threats and although courts usually pardon offenders if they apologise, some politicians have been convicted in the past for disobeying or insulting judges.
It was unclear whether Khan would attend Tuesday's court hearing or send his lawyer.
Khan came to power promising to break the pattern of family rule in Pakistan. His opponents contend he was elected with help from the powerful military, which has ruled the country for half of its 75-year history.
Since his ouster, Khan has also demanded early elections and vowed to oust Sharif's government through "pressure from the people".
