Saleh Muslim, a top Kurdish politician, has "full citizenship rights" as a Syrian national and was visiting Europe in an official capacity, the PYD party said.
In a statement, the party accused the Turkish state of "demanding the arrest of individuals who are not its citizens ... without any legal justifications".
Turkey has been seeking Muslim after a Turkish court charged him with "breaking the state and country's unity" and other offences.
Turkish President Tayyip Erdogan said that he hoped the Czech Republic would extradite Muslim to Turkey, adding Turkey did not have problems with Kurdish people, but rather "terrorists".
"Our hope is that the Czech Republic will extradite him to Turkey and justice will be served," Erdogan said. "When he is extradited, they will see how justice is implemented."
Turkey launched a military offensive last month in Syria's Afrin region against the Kurdish YPG militia, the PYD's armed affiliate, which it deems a menace on its border.
Muslim formerly headed the PYD, the major component of a coalition that governs Kurdish-held autonomous parts of northern Syria, including Afrin.
Ankara sees the PYD and YPG as extensions of the outlawed Kurdish PKK movement, which has waged a decades-long insurgency on Turkish soil - though the groups say they are independent.
In a statement on Twitter, Czech police said a 67-year-old man had been arrested in Prague at the request of the Turkish Interpol, but did not give a name for the suspect.
A statement from the TEV-DEM coalition, of which Muslim is a member, said Turkey had issued an arrest warrant for him and he was detained on Saturday.
Turkey's justice ministry said it had started efforts for Muslim to be extradited to Ankara, and had demanded that Czech authorities capture and arrest Muslim.
"Upon finding the person in question was in the Czech Republic, the necessary contacts were made and it was demanded that he be captured and arrested to be extradited back to our country," the ministry said in a statement.
Turkey's justice, interior and foreign ministries are working to secure the extradition of Muslim, Turkish Deputy Prime Minister Bakir Bozdag said, adding that Muslim was in detention in Prague.
Speaking to reporters, Bozdag, who is also the main government spokesman, said the Turkish and Czech foreign ministers would discuss the issue.
Ankara had previously demanded that Muslim face an Interpol Red Notice, an international arrest warrant circulated to member countries listing persons wanted for extradition.
(Reporting by Ellen Francis in Beirut, Tuvan Gumrukcu in Ankara and Michael Kahn in Prague; Editing by Larry King)