Local news media showed about 10 buildings set ablaze in the southern tourist town of Panguipulli following the shooting on Friday, and authorities reported other protests in Santiago the capital.
Police said 27-year-old Francisco Martínez Romero resisted police at a routine identity check.
A video circulated widely on social media showed an officer shooting toward the feet of the man, who was carrying and sometimes waving what appeared to be two blunt machetes used in his performance. After a moment, he leaped out and rushed toward the officer. Several shots were fired and the man collapsed in the street.
A local judge ordered the officer, who was not identified, held for investigation for two days.
The video angered some in the country, which has seen repeated controversies over allegations of police brutality against protesters in recent years. The National Human Rights Institute says that more than 450 people suffered eye damage from supposedly non-lethal projectiles fired by police during street protests that erupted in 2019.