Saleh Muslim was detained at a Prague hotel on Saturday night under an international arrest warrant issued by Ankara.
Turkey says Muslim is responsible for a 2016 bombing in Ankara which killed 29 people.
But Kurds say the charges are politically motivated.
“It is totally ridiculous,” says Hisyar Özsoy an MP for the HDP, a left-wing party which campaigns for Turkey's minorities, especially Kurds.
“At the core of this whole operation is Turkey’s anti-Kurdish stance in Middle Eastern politics.”
Turkey launches Afrin offensive
Muslim is the former co-chair of the Syrian Kurdish Democratic Union Party (PYD).
The party has close ties with the Kurdistan Workers Party (PKK), which is outlawed in Turkey for fighting for Kurdish self-rule.
Syrian Kurds have already declared autonomous rule in the chaos of the civil war. Turkey fears that this proto-state will be used as a rear-base for the PKK.
Last month the Turkish military launched an offensive against Kurdish militias on the Syrian side of the border.
Muslim was in Prague for a meeting on the Syrian conflict at the behest of US officials.
He was due to leave on Sunday.
“I think somebody has made a mistake,” says Bill Park, a Turkey specialist and visiting professor at King’s College, London.
“Maybe the organisers of the conference he was attending didn’t understand the implications of inviting him and representatives of the Turkish government.”
Political use of Interpol
What is clear is that Turkey has increasingly used the international police organisation Interpol’s Red List to try to catch critics of President Recep Tayyip Erdogan abroad.
“After the coup attempt in July 2016, the Turkish government began using Interpol as a diplomatic tool to hunt down members of the opposition,” says Emre Demir, a Turkish journalist based in Paris.
“Not just Kurdish dissidents, but also Gülenists [supporters of exiled preacher Fethullah Gülen whom the government says planned the coup], seculars and liberals. It’s part of an ongoing purge in Turkey.”
30 life sentences
Turkey says Muslim played a major role in the 2016 bombing in Ankara, which killed 29 people. He has been charged with terrorism offences and, if convicted, could face up to 30 life sentences.
Muslim himself says the charges have been trumped up.
Analysts say it is unlikely that the Czech authorities will grant the extradition request.
“There are many reasons why a European judicial system would raise a question about whether Muslim would receive a fair trial in Turkey,” says Park.
“It’s also the case that he’s not a Turkish citizen, he’s Syrian. So it’s unclear what right Turkey has to demand his extradition.”