Nearly 100 police officers and 55 civilians were injured and dozens of stations and public vehicles damaged or set alight, the government said. There were 70 arrests, mostly in Bogota.
Demonstrators were protesting the death this week of lawyer and father of two Javier Ordonez, 46.
The video, filmed by Ordonez's friend, shows him pinned to the ground by officers and subjected to successive electric shocks as he begs "Please, no more."
Police say Ordonez was found drinking alcohol in the street with friends in violation of coronavirus distancing rules. He was taken to a police station in western Bogota where his family allege he suffered further abuse. He died later in hospital.
The two officers involved have been suspended pending an investigation, the government has said. An autopsy is pending.
Authorities said they are investigating the deaths of the seven civilians in the protests - five in Bogota and two in Soacha. The dead include a 17-year-old boy.
"What we are facing here is a mass act of vandalism and violence," defense minister Carlos Holmes Trujillo told journalists. "What we are facing are unacceptable actions."
President Ivan Duque has said there can be no tolerance for abuse of authority, but the government called for Colombians not to "stigmatize" police officers.
Left-wing Bogota mayor Claudia Lopez has been more critical of the police, saying violence "isn't about bad apples."
She urged protesters to refrain from violence.
"Destroying Bogota will not fix the police," she said on Twitter on Thursday. "Let's concentrate on achieving justice and structural reform."Bogota's police will be reinforced with 1,600 more officers, more than half of whom will come from other regions, and 300 soldiers, the defense ministry said.