The interior minister tweeted in the early hours that Khan had to "face the law for threatening and hurling abuses at the Magistrate and Police officers".
Khan had criticised them at a rally on Saturday, over the arrest and alleged torture of a close aide.
"Islamabad Inspector General and Deputy Inspector General, we will not spare you, we will file a suit against you. And magistrate Zeba Chaudhry, you should also get ready as we will take action against you. You all should be ashamed."
Pakistan authorities booked the aide last week on sedition charges, accusing him of inciting mutiny in the military.
Khan has been making fiery speeches to gatherings across the South Asian nation.
The one-time cricket star has been pushing for new elections after being ousted from power in April through a parliamentary vote.
His address on Saturday also triggered a ban by Pakistan's electronic media regulator on the live TV broadcast of Khan's speeches, which it described as "hate speech" against state institutions.
Then, on Sunday evening, Khan accused the government of going even further to block YouTube temporarily, to deny live access to his speech at a political rally.
The Pakistan Telecommunication Authority, which regulates the internet, did not immediately respond to a request for comment.
Reuters could not immediately reach Khan to seek comment.
