In the incident local police called a "terror attack," a van slammed into pedestrians near Catalunya Square in Barcelona's Las Ramblas district, a busy tourist area.
Two people have been detained, police said.
Tillerson said this incident has "the hallmarks, it appears, of yet another terrorist attack."
ISIS has since claimed responsibility for the attack.
To terrorists around the world, Tillerson said, we are "resolved to find you and bring you to justice."
Tillerson added that the U.S. stands ready to assist authorities in Barcelona.
President Donald Trump condemned the attack in a tweet, encouraging Spain to "be tough and strong" and saying the U.S. "will do whatever is necessary to help."
Vice President Mike Pence tweeted that he is "sickened" by the "horrific" attack and that the U.S. vows to work with allies "to find those responsible & bring to justice."
Pence said today while on a trip to Panama, "Whatever inspired today's terror attack, the United States stands ready to assist the people of Spain and find and punish those responsible.
"On this dark day," Pence added, "our prayers and the prayers of all the American people are with the victims, their families and the good people of Spain."
First lady Melania Trump also offered her condolences, tweeting, "Thoughts and prayers to #Barcelona."
Former President Barack Obama tweeted, "Michelle and I are thinking of the victims and their families in Barcelona. Americans will always stand with our Spanish friends."
Speaker Paul Ryan tweeted, "Pure evil in #Barcelona. We stand with the people of Spain, and send our prayers to the victims of this horrible terrorist attack."
House Majority Whip Steve Scalise tweeted, "Jennifer and I are praying for those killed and injured in the terrorist attack in Barcelona. This evil has no place in our world."
House Minority Leader Nancy Pelosi tweeted, "My thoughts are with all suffering after the terror attack in #Barcelona. Praying for the victims, their loved ones and the people of Spain."
Sen. Ted Cruz, R-Texas, tweeted, "Heidi and I send our deepest condolences to the victims of this horrific terror attack in Barcelona and their families."
Sen. Marco Rubio, R-Fla., tweeted, "I condemn today's horrific terrorist attack in #Barcelona. My thoughts and prayers go to the victims and their families."
Sen. John McCain, R-Ariz., tweeted, "Praying for the victims of the #BarcelonaAttack & their families - the US stands with the people of #Spain."
Rep. Adam Kinzinger, R-Ill., tweeted, "We must destroy evil & #terrorism wherever it exists. Tonight we stand w/ our allies in #Barcelona & pray for the victims & their families."
Sen. Jim Inhofe, R-Okla., tweeted, "Praying for the victims, families and first responders in Barcelona."
New York City mayor Bill de Blasio tweeted, "Our thoughts are with the people of Barcelona right now. The NYPD is closely monitoring the incident."
ABC News' Erin Dooley and Meghan Keneally contributed to this report.