BBC reports Protests are erupting nationwide, and at least one person has been killed in the city of Quetta.
The United States and UK have called for adherence to the "rule of law".
Khan was arrested by security forces at the High Court in the capital, Islamabad.
Dramatic footage showed dozens of officers arriving and detaining the 70-year-old, who was bundled into a vehicle and driven away.
He was appearing in court on charges of corruption, which he says are politically motivated.
Mobile data services in the country were suspended on the instructions of the interior ministry on Friday as protests grew, many of them taking place in front of army compounds.
Pakistan's army plays a prominent role in politics, sometimes seizing power in military coups, and, on other occasions, pulling levers behind the scenes.
Many analysts believe Khan's election win in 2018 happened with the help of the military. Now in opposition, he is one of its most vocal critics, and analysts say the army's popularity has fallen.
Footage from Lahore posted on Twitter appeared to show a crowd breaking into the military corps commander's house], destroying furniture and belongings inside.
Speaking from Washington, the US Secretary of State Antony Blinken said he wanted to make sure that "whatever happens in Pakistan is consistent with the rule of law, with the constitution".
UK Foreign Secretary James Cleverly, speaking alongside Blinken, noted that Britain enjoyed "a longstanding and close relationship" with Commonwealth member Pakistan, and wanted to "see the rule of law adhered to".
On Tuesday evening, supporters of Imran Khan gathered outside the Pakistan High Commission in London to protest against his arrest.
Khan was ousted as PM in April last year and has been campaigning for early elections since then.
General elections are due to be held later this year.
Speaking to the BBC's Newshour, Khan's spokesman, Raoof Hasan, said he expected "the worst" and that the arrest could plunge the country "into chaos and anarchy".
"We're facing multiple crises. There is an economic crisis, there is a political crisis, there is a cost of livelihood crisis and consequently this occasion will be a catharsis for them to step out and I fear a fair amount of violence is going to be back," he said.
A member of Khan's legal team, Raja Mateen, said undue force had been used against him at the court.
"Khan went into the biometric office for the biometrics. The rangers went there, they broke the windows, they hit Khan on the head with a baton," said Mateen.
Khan's Pakistan Tehreek-e-Insaf (PTI) party called on its supporters to protest. In the hours after he was detained, violence was reported from cities including Lahore, Karachi and Peshawar.
On the streets of Islamabad, hundreds of protesters blocked one of the main highways in and out of the capital.
People pulled down street signs and parts of overpasses, lit fires and threw stones. During the hour or so that the BBC was there, no police or authorities were visible.
Protesters said they were angry about Khan's arrest.
"This is absolutely the last straw," said Farida Roedad. "Let there be anarchy, let there be chaos. If there is no Imran, there's nothing left in Pakistan. No one is there to take over."
Writing on social media, police in Islamabad said five police officers had been injured and 43 protesters arrested.
It said at least 10 people, including six police officers, had been injured in the south-western city of Quetta in clashes between Khan's supporters and security forces - with one protester killed.
A statement from the inspector general of Punjab police said the arrest of Khan had been ordered because he was accused of "corruption and corrupt practices".
The case involves allegations over the allotment of land in the so-called Al-Qadir Trust, which is owned by Khan and his wife, Dawn newspaper reported.
Khan, who is being held at an undisclosed location, denies breaking any law.
In a video message filmed as he travelled to Islamabad - and released by the PTI before his arrest - Khan said he was ready for what lay ahead.
"Come to me with warrants, my lawyers will be there," he said. "If you want to send me to jail, I am prepared for it."
Security was tight in the centre of the capital for the former PM's court appearance.
Dozens of cases have been brought against Khan since he was ousted from power.
The security forces have tried to detain him on a number of previous occasions at his Lahore residence, but were blocked by his supporters, resulting in fierce clashes.
On Tuesday, police had blocked roads into Islamabad, so the number of supporters with Imran Khan was not as high as on previous occasions, making it easier to arrest him.
He was elected prime minister in 2018, but fell out with Pakistan's powerful army. After a series of defections, he lost his majority in Parliament. He was ousted after he lost a confidence vote in April 2022, four years into his tenure.
Since then, he has been a vocal critic of the government and the country's army.
In October, he was disqualified from holding public office, accused of incorrectly declaring details of presents from foreign dignitaries and proceeds from their alleged sale.
The next month, he survived a gun attack on his convoy while holding a protest march.
On Monday, the military warned him against making "baseless allegations" after he again accused a senior officer of plotting to kill him.
Policemen retreat after firing teargas shells towards Pakistan Tehreek-e-Insaf party activists and supporters of former Pakistan's Prime Minister Imran Khan. Photo: ASIF HASSAN / AFP