The Aurora Police Department said on Twitter that protesters were walking on Interstate 225 on Saturday when a vehicle drove through.
Police said a demonstrator fired a weapon, striking at least one person who was taken to a hospital in stable condition.
Authorities said the vehicle was towed and they are investigating.
Protesters also broke windows to the courthouse and a fire was started in an office, police said, with demonstrators ordered to leave after an unlawful assembly was declared.
Tensions have been heightened at recent protests against racial injustice since federal officials were sent to quell demonstrations in Portland, Oregon.
Thousands of protesters gathered outside the federal courthouse in Portland into the early hours of Saturday.
The Federal Protective Service had declared the gathering as “an unlawful assembly” and said officers had been injured.
Meanwhile, police declared a riot in Seattle on Saturday.
Protests against police brutality have spread around the world following the May 25 death of George Floyd, a black man in Minnesota who died after a white officer held him to the ground with a knee to his neck.
In Colorado, protesters have been drawing attention to the death of Elijah McClain, who was stopped by police while walking down an Aurora street in August 2019 after a 911 caller reported him as suspicious.
Police placed him in a chokehold, and paramedics administered 500 milligrams of ketamine, a sedative, to calm him down.
He went into cardiac arrest, was later declared brain dead and taken off life support.
