The PYD accused Ankara of "demanding the arrest of individuals who are not its citizens.without any legal justifications".
Czech authorities arrested Muslim in Prague on Saturday.
Turkey has submitted documents to Czech Republic authorities formally requesting the extradition of the former leader of the PYD, Deputy Prime Minister Bekir Bozdag said on Monday.
Turkey sees the YPG and PYD as the Syrian branch of the Kurdistan Workers Party (PKK), which for over three decades has waged an insurgency against the Turkish state and is banned by Turkey, the U.S. and the European Union as a terror group.
The Turkish interior ministry had offered a bounty of almost $1m on Muslim, who is listed as one of the "most wanted terrorists" in Turkey.
Billy Graham to lie in honour at US Capitol - House speaker
By his final crusade in 2005 in New York City, he had preached in person to more than 210 million people worldwide. Graham's funeral on March 2, which according to local reports had been " in the works for years ", will be private.
Muslim was put on Turkey's most-wanted list earlier in February with a $1 million reward.
"The president. stressed that the humanitarian truce applied to all of Syria, including Afrin, and should be implemented everywhere and by all without any delay", Macron's office said after a call with Turkish President Tayyip Erdogan.
Muslum was expected to appear before a Prague court on Tuesday, which would then decide if he would remain in detention, Turkish Ambassador in Prague Ahmet Necati Bigali told Turkey's Anadolu Agency.
The arrest comes as Turkey presses a military operation against the Kurdish People's Protection Units (YPG) militia - the military wing of the PYD - in the western enclave of Afrin in northern Syria. The PKK is branded a terrorist group by the United States and European Union as well as by Turkey, but the YPG is Washington's main military ally in northeast Syria. PYD said Muslim was a key figure in the search for a political solution in Syria and appealed for his release, describing his arrest as "immoral".