The 59-year-old Yalcin was seized on Thursday at passport control at Barcelona airport, as he prepared to board a flight for London. According to his partner, Turkey had issued a wanted notice through the international police network Interpol.
"The Spanish courts have told him that Turkey is accusing him of organising terror while at the Odak Dergisi newspaper in 2010, his partner, who has spoken to Yalcin, told TT.
She said that Turkey had provided recordings of phone conversations made over the internet as evidence.
Sweden's foreign ministry is seeking a meeting with Yalcin.
The pressure group PEN, which fights for authors' freedom of expression, has demanded that the Swedish government and the European Union act to prevent Yalcin being deported to Turkey.
She told Radio Sweden that Yalcin risked joining a list of more than 200 Turkish writers and journalists currently on trial or imprisoned by Turkey's government.
"Turkey is having a crackdown at all these activities," she said. "There are several cases where Turkey hasn’t presented any valid allegations and certainly no proof for their accusations. The accusations are in a lot of cases crazy."
Sweden's foreign ministry confirmed on Monday that a Swedish national was being held.
"Our embassy is monitoring this case," a foreign ministry spokesman told TT.