The letter is signed by Swedish MEPs Max Andersson and Bodil Valero of the Green Party; Malin Björk of the Left Party; Fredrick Federley of the Centre Party; Anna Hedh, Olle Ludvigsson, Jens Nilsson and Marita Ulvskog of the Social Democrats; and Soraya Post of Feminist Initiative.
It calls on Spain to release Yalcin, who is being held on Turkey's orders.
"The only crime Mr Yalcin is guilty of is criticizing Mr Erdogan," they write.
Yalcin, who has lived in Sweden since 1984 and has dual Swedish-Turkish citizenship, was arrested on August 3rd at Barcelona's El Prat airport and is being held while a Spanish court decides whether to extradite him or not.
Jonathan Lundqvist, head of Reporters Without Borders in Sweden, has criticized the arrest as an attempt by Turkish President Recep Tayyip Erdogan "to extend his power beyond the country's borders".
"He wants to show that he can get at critics even if they are not in the country. This is an abuse of international police cooperation, which risks having major consequences," he said in a statement last month.
Yalcin, who writes for Odak, a left-wing online magazine critical of the government in Ankara, is wanted in Turkey based on two allegations, one relating to insulting Erdogan and another relating to terrorism.
His arrest comes as alarm grows over press freedom in Turkey under Erdogan, with foreign reporters also being caught up in the crackdown.