The suspect, identified as 45-year-old Mohamed Sabry Soliman, yelled "Free Palestine" and used a makeshift flamethrower in the Sunday attack, said Mark Michalek, the special agent in charge of the Denver field office.
Soliman was taken into custody.
No charges were immediately announced but officials said they expect to hold him "fully accountable".
Soliman was also injured and was taken to the hospital.
Video from the scene showed a witness shouting: "He's throwing Molotov cocktails", as a police officer with his gun drawn advanced on a bare-chested suspect with containers in each hand.
The attack took place at the popular Pearl Street pedestrian mall, a four-block area in downtown Boulder, where demonstrators with a volunteer group called Run For Their Lives had gathered to draw attention to the hostages who remain in Gaza.
The war between Israel and Hamas continues to inflame global tensions and has contributed to a spike in anti-Semitic violence in the United States.
It occurred more than a week after the fatal shooting of two Israeli embassy staffers in Washington by a Chicago man who yelled "I did it for Palestine, I did it for Gaza".
FBI leaders in Washington said they were treating the Boulder attack as an act of terrorism, and the Justice Department — which leads investigations into acts of violence driven by religious, racial or ethnic motivations — decried the attack as a "needless act of violence, which follows recent attacks against Jewish Americans".
"This act of terror is being investigated as an act of ideologically motivated violence based on the early information, the evidence, and witness accounts. We will speak clearly on these incidents when the facts warrant it," FBI Deputy Director Dan Bongino said in a post on X.
Police in Boulder were more circumspect about a motive.
Police Chief Steve Redfearn said it "would be irresponsible for me to speculate" while witnesses were still being interviewed but noted the group that had gathered in support of the hostages had assembled peacefully and that injuries of the victims — ranging from serious to minor — were consistent with them having been set on fire.
The scene shortly after the attack was tense, as law enforcement agents with a police dog walked through the streets looking for threats and instructed the public to stay clear of the pedestrian mall.
Colorado Governor Jared Polis said in a statement that he was "closely monitoring" the situation, adding that "hate-filled acts of any kind are unacceptable".
with reuters
