A spokesman for the National Accountability Bureau (NAB), which has in the past investigated, put on trial and jailed all those who served as prime minister since 2008, said Khan was expected at the agency's Rawalpindi headquarters, near Islamabad.
It was not clear if Khan, who denies the charges, would heed the summons. A spokesman for Khan's party, the Pakistan Tehreek-e-Insaf, was not immediately available for a comment.
Khan's May 9 arrest by paramilitary troops triggered a wave of violence that deepened political instability in the South Asian nation of 220 million. Pakistan has also been facing its worst ever economic crisis, with a long delay in securing critical IMF funding.
The Supreme Court ordered Khan's release on bail last Friday, and another court on Wednesday extended his protective bail until May 31.
His wife Bushra Khan, commonly known as Bushra Bibi is also on bail until May 23.
On Wednesday, Khan said that police had surrounded his house in Lahore, in Punjab province, and that he expected to be re-arrested soon, after the government warned him to hand over supporters who it blamed for attacks on the army.
Punjab's information minister Amir Mir said the government did not have any plans to arrest Khan as he had been given bail by court. "All we want (is) him to hand over the terrorists hiding at his home," he said.
Mir said intelligence and law enforcement agencies had identified that up to 40 people accused of attacking military installations were hiding at Khan's home. He said Khan had 24 hours to surrender the suspects or face a "police operation".
Khan has said authorities could search his home but only with legal warrants from a court, and has denied sheltering anyone involved in the violence.
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