While stressing that the information was "very preliminary", Boulder Police Chief Stephen Redfearn said the man was apprehended on Sunday following calls to the police of someone with a weapon who was "setting people on fire".
Redfearn said he wasn't in a position to identify the suspect yet, saying he'd been taken to the hospital.
There were multiple injuries among the victims, ranging "from very serious to more minor", he said.
The attack occurred in the vicinity of a walk to remember the Israeli hostages being held in Gaza.
FBI Director Kash Patel, in a statement, described the incident as a targeted terror attack and said agents were on the scene.
Redfearn, however, said it was too early to speculate about a motive.
"We are not calling it a terror attack at this moment," he said.
"This was a beautiful Sunday afternoon in downtown Boulder on Pearl Street and this act was unacceptable," he said.
"I ask that you join me in thinking about the victims, the families of those victims, and everyone involved in this tragedy."
The incident comes amid heightened tensions in the United States over Israel's war in Gaza, which has spurred both a an increase in anti-Semitic hate crime as well as moves by conservative supporters of Israel led by President Donald Trump to branded pro-Palestinian protests as anti-Semitic.
His administration has detained protesters without charge and cut off funding to elite US universities that have permitted the demonstrations.
It also follows the arrest of a Chicago-born man in the fatal shooting of two Israeli embassy employees in Washington, DC.
Someone opened fire on a group of people leaving an event hosted by the American Jewish Committee, an advocacy group that fights anti-Semitism and supports Israel.
The shooting fuelled polarisation in the United States over the war in Gaza between supporters of Israel and pro-Palestinian demonstrators.
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