Their investigation comes after he accused the police and judiciary of detaining and torturing his close aide.
Tensions are high in the country, with the former leader's supporters gathering outside his house vowing to "take over" if he is arrested.
Since being ousted from power in April, Mr Khan has been a vocal critic of the government and the country's army.
Police announced the charges after the cricketer-turned-politician accused authorities of torturing his close aide, who is himself being detained under sedition charges.
In a public speech on Saturday, Mr Khan condemned Islamabad's police chief and a female judge for the detention and alleged mistreatment of his party colleague, Shahbaz Gill.
"You should also get ready as we will take action against you," he said in the speech, referring to the pair directly.
Officials accused Mr Khan of breaching the country's anti-terrorism act for allegedly making threats against the state officials.
Hundreds of the former prime minister's supporters gathered outside his home in Islamabad after news of the investigation broke, vowing to "take over" the capital if police tried to detain him.
Police who were present at the scene said they were not there to arrest the former leader, but to maintain law and order.
The case comes at a time of heightened tension between Pakistan's government and Mr Khan, who was ousted from power in April in a no-confidence vote.
Since then, the former leader has toured the country to deliver a series of fiery speeches calling for fresh elections and fiercely criticising both the government and the army.
On Saturday, Pakistan's media regulator announced that television channels would be banned from broadcasting his speeches live, accusing Mr Khan of hate speech against state institutions.
The former leader claims the government is trying to censor him. On Sunday, he criticised the ban at another political rally in the city of Rawalpindi.
"What crime has Imran Khan committed? I will never accept this gang of thieves," he told his supporters.
Mr Khan later accused the government of blocking access to YouTube halfway through the speech in an effort to prevent people from listening to him live.
Despite being ousted from power in a no-confidence vote earlier this year, Imran Khan continues to count on the support of many Pakistani voters.
Last month, his PTI party stunned rivals by taking control of a crucial provincial assembly in Punjab, defeating the PML-N party in what was expected to be an easy win for them.
Many saw July's by-election victory as a signal of Mr Khan's continued popularity at the ballot box - and a foretaste of what could happen if the early elections that he is seeking were to be held.
The charismatic politician was elected prime minister in 2018, but fell out with Pakistan's powerful army towards the end of his tenure. After a series of defections, he lost his majority in parliament.
-- Courtesy of BBC News