The correspondent Taysir Alluni, who found fame in the Arab world for his exclusive reporting from Afghanistan during the US-led war on the Taliban in 2001, was arrested on Friday.
Spanish authorities said the detention came on the orders of judge Baltasar Garzon as part of an investigation into the operations of Islamist groups.
The arrest provoked a furious reaction from the network on Saturday.
"Aljazeera is open to all the players on the political scene, from (Usama) bin Ladin to (US President) George W Bush, without discrimination and without favour," said Jihad Ballout, spokesman for the news channel in the Qatari capital Doha.
"The arrest is all the more strange since over two months of holidays in Spain, Alluni interviewed several political leaders, including Prime Minister Jose Maria Aznar, and took part in several political meetings," Ballout said.
The arrest of Alluni in Granada on Friday "is only another link in a chain of pressures and persecution against Aljazeera to try to influence its professional stance", he said.
"The arrest is a new stage in the harassment of which journalists in general and those from Aljazeera in particular are victim," Ballout said.
"For us, Alluni is an excellent journalist. We know nothing about his political ideas ... that is something you will have to ask him"
"For us, Alluni is an excellent journalist. We know nothing about his political ideas ... that is something you will have to ask him," the spokesman said, condemning "the behaviour of the Spanish authorities in arresting a well-known journalist, just a day before he was to return to Doha.
Aljazeera said it had appointed a lawyer to defend Alluni, but had been unable to contact the Spanish authorities.
The station also launched "a campaign to support Alluni, targeting non-governmental organisations who defend press freedom".
Judge Garzon and Spanish state prosecutor Pedro Rubira suspect Alluni of involvement in "the organisation of, support for and infrastructure of this cell," according to the warrant for his arrest.
Alluni also stands suspected of "furnishing al-Qaida with funds in Afghanistan," where he was an Aljazeera correspondent during the 2001 US-led war which brought the end of Taliban rule.
Police said Alluni was suspected of having links to members of Bin Ladin's al-Qaida network, including Imad Eddin Barakat Yarkas, alias Abu Dahdah.
Barakat was arrested on suspicion of being the ringleader of an eight member-strong Islamist cell which Spanish authorities claim to have dismantled in November 2001.
The cell is said to have helped prepare the 11 September attacks, though US authorities have not applied for Barakat's extradition.
Spanish authorities added that Alluni was expected to appear before a judge by Monday.