Police said a man was taken into custody on Sunday with the FBI describing the incident as a "targeted terror attack".
Information on the attack, which occurred near a walk to remember the Israeli hostages who remain in Gaza, was "very preliminary", Boulder Police Chief Stephen Redfearn said.
The man was apprehended following calls to police about someone with a weapon who was "setting people on fire", he said.
"That's consistent with the injuries we found on the scene. There's a lot of witnesses we're interviewing."
The victims' injuries range from serious to minor.
While FBI Director Kash Patel described the incident as a "targeted terror attack," Redfearn stressed it was too soon to speculate about a motive.
"We are not calling it a terror attack at this moment," Redfearn said.
"This was a beautiful Sunday afternoon in downtown Boulder on Pearl Street and this act was unacceptable," he said.
The attack took place at a pedestrian mall that's popular with tourists and college students and occurred as law enforcement authorities in the US grapple with a spike in anti-Semitic violence.
Last week, a man was arrested over the fatal shooting of two Israeli embassy staffers and shouted "Free Palestine" as he was being led away by police.
Multiple blocks of the pedestrian mall area were evacuated by police.
Colorado Governor Jared Polis said in a statement he was "closely monitoring" the situation, adding that "hate-filled acts of any kind are unacceptable".
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