A spokesman for the governing Nationalist Basque Party (PNV) said Mr Garzon, a prominent Supreme Court magistrate, had encroached on the competence of the Basque authorities and violated the right to freedom of assembly.
The widely trailed move follows Judge Garzon's decision to suspend Batasuna over its alleged links to the Basque guerrilla group, ETA.
The PNV also said the judge had lost all sense of balance when he announced he was investigating ETA for alleged ethnic cleansing and crimes against humanity.
The Spanish authorities, who have imposed a separate ban on Batasuna, have accused the PNV of colluding with terrorists.
The Basque Government said last month it would sue Judge Garzon after he slapped a three-year ban on Batasuna, which the Spanish Government says is the political wing of the armed ETA group, and prohibited all subsequent protests against his ruling.
A Basque government spokesman last month called the decision unjust and excessive, saying it "incriminated the majority of the Basque population".
'Ethnic cleansing'
In a writ issued on Thursday, Judge Garzon alleged that Batasuna was also involved in low-level ethnic cleansing by driving non-nationalists from the Basque country.
He alleges that their aim is to ensure a vote in favour of independence should the region hold a referendum.
This so-called purification of a society would, in his view, constitute a crime against humanity under international law.
The judge has asked the Spanish and Basque authorities for a list of those professionals, policemen and journalists who have left the Basque country because of violence and intimidation by ETA.
The Spanish El Mundo newspaper, close to the government in Madrid, criticised the writ, saying: "Garzon anticipates the conclusions of his inquiry, then looks for arguments to corroborate them."
However, Spanish Vice-President Mariano Rajoy welcomed Judge Garzon's order as a suitable response to alleged human rights violations in the Basque province.
The launch of this inquiry underlines Baltasar Garzon's determination to see a final end both to Batasuna and to ETA, says BBC Madrid correspondent Clare Marshall.