The Turkish citizen's name will not be publicized before the family is informed.
At least 13 people were killed and more than a hundred injured when a white van ploughed into a crowd in the Spanish city on Thursday.
The driver of the vehicle is still on the run.
Spanish police also shot five suspected terrorists dead in a later operation in Cambrils town, close to Barcelona.
Seven people, including police, were injured when car drove into them in the early hours of Friday morning, after the Barcelona attack.
Catalonia's regional leader, Charles Puigdemont, later told local media explosive belts the dead terrorists had been wearing turned out to be fakes.
Turkey's President Recep Tayyip Erdogan offered his condolences to Spain's King Felipe on Thursday following the attacks which he said "showed the brutal face of terrorism once again."
In a written statement Turkish Foreign Ministry condemned the attack, saying that Turkey will maintain solidarity with Spain, which is a friend and an ally of Turkey.
"We extend our deepest condolences and wish fortitude to the families of those who lost their lives and speedy recovery to those wounded in these heinous attacks which display once again the brutal face of terrorism and target all humanity," the statement said.
According to Spanish media, Daesh claimed responsibility for the attack that involved a van ploughing into people at Las Ramblas, a street in central Barcelona popular with both tourists and locals.
A minute's silence is to be held at Placa de Catalunya, the scene of the Barcelona attack, at midday local time (GMT1100) on Friday.
Catalan police have warned access will only be permitted on food and those attending should not wear backpacks.