The Scottish government has written to the Spanish ambassador voicing "regret" at the move, but has stressed that it has no choice but to follow due process and comply with the warrant.
The case of a former Catalan separatist politician fighting extradition to Spain from Scotland is creating political complications at an awkward time for Edinburgh's pro-independence government.
Clara Ponsati, the former Catalan minister facing extradition from the United Kingdom to Spain on charges of fomenting rebellion, has described the claims as a "grotesque distortion of the truth".
A rift between the Scottish and United Kingdom governments has opened up over the fate of a political fugitive from Catalonia who is facing extradition to Spain.
However, First Minister Nicola Sturgeon has insisted she can not intervene in an independent legal extradition process.
"She is now attending a police station in Scotland and has said the outpouring of supportive messages and contributions has been truly inspirational to her and given her the drive, determination and spirit to take on this fight".
Scottish-based Prof Ponsati attended a police station in Edinburgh voluntarily on Wednesday morning after she was made the subject of a European arrest warrant last week.
Clara Ponsati, Catalonia's former education chief and now a professor at the University of St. Andrews, returned to Scotland in March after fleeing Spain with Puigdemont.
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Professor Ponsati, is being sought by the authorities in Madrid on charges of "violent rebellion and misappropriation of public funds" over her role in Catalonia's controversial independence referendum a year ago.
As Ponsati handed herself in at a Scottish police station to face charges which also include one of misuse of public funds over the banned independence vote, her lawyer said Ponsati believed she would not get a fair trial in Spain.
A Spanish judge last week issued global and European arrest warrants for Ponsati and other separatist leaders, including former regional president Carles Puigdemont.
Spanish national police said on Wednesday that two Catalan regional officers who were traveling with him had also been arrested.
The SNP, which runs the devolved government with powers over health, education and taxes, has requested a meeting with the Spanish ambassador in London to express its opposition to the treatment of politicians.
"Clara remains defiant and resolute and believes that the Spanish Government will never be able to crush the spirit of the Catalan people". This offence is punishable by up to 30 years imprisonment.
Held in front of Sheriff Nigel Ross at Edinburgh Sheriff Court, the hearing lasted less than 10 minutes and saw the academic granted bail and instructed to surrender her passport.
"Extradition is not about guilt or innocence".