Police announced the arrest of two suspects, identified as a Spaniard and a Moroccan, but said the driver was still on the run.
Witnesses told of scenes of chaos and horror, with bodies strewn along the famous boulevard as other people fled for their lives, screaming in panic.
The rampage yesterday in a city hugely popular with tourists from around the world is the latest in a wave of attacks in Europe where vehicles have been used as weapons of terror.
Regional interior minister Joaquim Forn said 13 people had died and another 100 were injured in what police were treating as a "terrorist attack", warning that the death toll could rise further.
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Foreigners were among the victims.
Las Ramblas is one of Barcelona's busiest streets, lined with shops and restaurants and normally packed with tourists and street performers until well into the night.
"When it happened I ran out and saw the damage," local shop worker Xavi Perez told AFP.
Witness Aamer Anwar told Britain's Sky News television 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."
Footage broadcast on Spanish television showed a white van, its front completely crushed, abandoned by its driver on a road surrounded by police cars.
Tom Gueller, who lives on a road next to Las Ramblas said he saw the vehicle speeding along the boulevard.
Ethan Spibey, a charity director on holiday, said he and several others 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."
Spain had until now been spared the kind of extremist violence that has rocked nearby France, Belgium and Germany.
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.
The Spaniard was arrested in Alcanar, about 200 kilometres south of Barcelona, the scene of an explosion in a house late yesterday that left one person dead and is believed to be linked to yesterday's assault.
"We suspect that they (the occupants) were preparing an explosive device," Josep Lluis Trapero of the regional Catalonia police told reporters.
In another incident yesterday, police shot at a vehicle that forced its way through a roadblock in Barcelona after the van attack, knocking down two officers.
Yesterday's attack drew condemnation from across the globe.
Spain's royal family vowed that their country would not be "terrorised" by extremists.
US President Donald Trump condemned the "terror attack" and said the Unied States will do whatever is necessary to help", adding: "Be tough & strong, we love you!"
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 shootings and bombings on Paris nightspots were claimed by the Islamic State, but it is believed to be the first IS claim of an attack in Spain.
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.