Former PYD leader Salih Muslim was detained in Prague yesterday amid accusations of collusion with Turkish intelligence.
Rumours circulated that Mr Muslim was being held at the insistence of Turkey.
The Syrian Kurd was added to the country's "most wanted list by the Turkish Interior Ministry earlier this month.
Mr Muslim had been placed on an Interpol "red list" by Turkey who also offered a $1 million bounty for his arrest.
Czech police confirmed they detained a 67-year-old foreigner who was wanted in Turkey, however, did not name the person in question.
The TEV-DEM coalition confirmed the detention of Mr Muslim and said it condemned "this illegal act." In a statement, TEV-DEM said the detention of Mr Muslim was “contrary to all international values and laws. “The Turkish state does not have the right to prosecute or arrest any person who is not their citizen. Mr Salih Muslim is a Syrian citizen."
It is reported that Turkey is preparing papers seeking the extradition of Mr Muslim and it is expected that a Czech court will rule on whether to agree to the request or release him.
Mr Muslim was a founder member of the Democratic Union Party (PYD) and stood down as its co-chair in 2017. He has since been appointed Foreign Relations spokesman for TEV-DEM, holding meetings with European parliamentarians regarding Operation Olive Branch, Turkey's deadly assault on Afrin which has killed more than 200 civilians and maimed and injured many more.
He was in Prague for a conference when it is alleged that Turkish security services circulated photographs of Mr Muslim and demanded his arrest.
Turkey lists the PYD as a terrorist organisation linked to the Kurdistan Worker's Party (PKK). Turkish President Recep Tayyip Erdogan wants European countries and the US to ban the PYD and drop support for the People's Protection Units (YPG) in northern Syria. In November 2016 Turkey issued an arrest warrant for Mr Muslim, however despite appeals, Interpol refused to issue a European warrant.
At the time Mr Muslim was meeting FCO officials in Britain and addressed MPs and others in the Houses of Parliament. He has good relations with a number of European leaders and the PYD has an office in Brussels. The November 2016 arrest warrant claimed that Mr Muslim was wanted in connection with the bombing of a military convoy in Ankara which killed 28 people however the PYD had condemned the attack which the Kurdistan Freedom Falcons (TAK) claimed responsibility for.
His detention comes at a time when Turkey's war on Afrin is intensifying. President Recep Tayyip Erdogan has been accused of wanting to "ethnically cleanse" the area of Syria known as Rojava by Kurds. Turkey denied recent allegations that it had used chemical weapons in Afrin. Turkey's offensive has drawn widespread condemnation.
Mr Muslim slammed Mr Erdogan and tweeted a photograph he claimed were children killed by Turkish bombs with the caption "Turkey president – child killer.” TEV-DEM called for the United Nations to condemn the arrest and for international protests.