A Catalan government official confirmed the current death toll on Twitter.
Police are hunting for the driver of a white Fiat van, who fled on foot after the incident in Las Ramblas.
The vehicle careered into terrified pedestrians in the busy tree-lined promenade, one of the most popular parts of the city, visited by tourists and locals alike.
Government officials confirmed one fatality and said at least 32 people had been injured, seven of them seriously.
The vehicle hit pedestrians in the busy tree-lined promenade in the centre of the city, the Ministry of the Interior said.
The street is one of the most well-known and popular parts of the city, visited by tourists and locals alike.
Images posted on social media appear to show people being tended to as they lay on the street.
The driver of the van is reported to have fled on foot and Spanish authorities have warned people to avoid the area.
Catalonia’s interior minister Joaquim Forn told reporters: “Unfortunately the number of fatalities will likely rise.”
According to unconfirmed reports, two attackers were holed up in a bar near the scene.
Lawyer and University of Glasgow rector Aamer Anwar was walking La Ramblas when he heard screaming.
He said a shopkeeper told him five or six people were badly injured and described the scene as “chaos”.
Mr Anwar said: “I had been to the Cathedral and walking down Las Ramblas for something to eat. Part of it was in the shade so I decided to keep walking down and literally within 10 seconds there was a crashing noise.
“I turned around and people were screaming - I could see a woman screaming with her kids - people started running and jumping into shops. I ran for about 50 or 100 metres and stopped to see what was happening. The police were very quickly on the scene and getting people to move back.
“I could see chaos right at the top area and I spoke to a shopkeeper who had run down and was screaming. He was Bengali so I spoke to him in Urdu and he said a van had driven into a crowd and he thought there were five to six people very seriously injured.”
Barcelona police have said the Las Ramblas van crash is a “terrorist attack”
Steve Garrett was in a nearby market and sheltered in a bakery with several others after streams of people ran inside.
One member of the group, who took refuge with him, said she had heard gunshots after the incident.
Mr Garrett told the BBC: “A very large number of people ran into the market area in a big kind of way, lots of screaming, lots of shouting.
“The security guards immediately responded. We ran into the bakery with four or five other people and ran straight upstairs and hunkered down whilst an enormous wave of people went through the market.
“Obviously coming from England it was reminding me a great deal of what happened in London, so we were very concerned about what might be going on next.
“The lady that was with us said she heard some gunshots.”
Mr Garrett said a “second wave” of people then entered the market, followed by armed police.
He said: “They seemed to sweep through the market area. They seemed to be looking for someone. They were going very carefully, very cautiously, stall to stall.”