Police said they had arrested two suspects after the assault, the latest in a wave of vehicle rampages across Europe in recent years.
The IS propaganda agency Amaq claimed that "soldiers" from the jihadist group carried out the attack, according to the Site Intelligence Group which monitors Islamist websites.
Witnesses told of the panic unleashed in an area thronging with local residents and tourists in Spain's second biggest city, as world leaders united in condemning the carnage.
One of the suspects was named by the police union as Driss Oukabir, but there were no further details and police denied earlier reports a perpetrator was holed up in a bar.
More From This Section
The famous Las Ramblas is one of Barcelona's busiest streets, lined with shops and restaurants and normally packed with with tourists and street performers until well into the night.
Police said there had been a "huge collision" between a van and pedestrians on the thoroughfare and a police source said officers were seeking a total of two suspects.
Witnesses told of scenes of horror, with bodies strewn along the boulevard as others fleeing for their lives.
"When it happened I ran out and saw the damage," local shop worker Xavi Perez told AFP.
"There were bodies on the ground with people crowding round them. People were crying. There were lots of foreigners."
Witness Aamer Anwar told Britain's Sky News television that he was walking down Las Ramblas, which he described as "jam-packed" with tourists.
"All of a sudden, I just sort of heard a crashing noise and the whole street just started to run, screaming. I saw a woman right next to me screaming for her kids."
But it was hit by what is still Europe's deadliest jihadist attack in March 2004, when bombs exploded on commuter trains in Madrid, killing 191 people in an attack claimed by Al Qaeda-inspired extremists.
Ethan Spibey, a charity director on holiday in the city, said he and several others had locked themselves in a nearby church.
"All of a sudden it was real kind of chaos... People just started running screaming," he told Sky. "There was kind of a mini stampede."
Tom Gueller, who lives on a road next to Las Ramblas said he saw the van speeding along the boulevard.
A Greek diplomat in the city said three nationals had been wounded -- a woman and her two children.
Today's attack, which followed similar incidents in Britain, Germany and France, drew widespread condemnation.
"The United States condemns the terror attack in Barcelona, Spain, and will do whatever is necessary to help," US President Donald Trump tweeted.
France's President Emmanuel Macron -- whose country has witnessed a series of bloody jihadist atrocities including a truck rampage in Nice in July 2016 that killed 86 people -- said his thoughts were with the victims of the "tragic attack".
The Nice carnage and other assaults including the 2015 Paris attacks on nightspots in the city were claimed by the Islamic State.
In another deadly vehicle attack in December, 12 people were killed when a man driving a truck ploughed into a crowd at a Berlin Christmas market.
Spain has emerged as a potential target for jihadists, with extremist websites mentioning it for historical reasons, since much of its territory was once under Muslim rule.
But they publicise every arrest of alleged jihadists, most of them detained for propaganda, recruitment for extremist groups or "glorifying terrorism."
According to the interior ministry, more than 180 "jihadist terrorists" have been arrested since 2015.