Additional Chief Metropolitan Magistrate (ACMM) Shunali Gupta granted the relief to Marie Emmanuelle Verhoeven subject to furnishing of a personal bond of Rs five lakh and two sureties of the like amount.
The magistrate also ordered Verhoeven to surrender her passport and not leave the national capital without its permission.
The court ordered that its decision be also forwarded to the Foreigners Regional Registration Office (FRRO) and the immigration department so that no fresh passport or exit permit is issued in her favour without its permission.
Verhoeven's challenge to the government's decision to extradite had reached the Supreme Court which on April 28 held that there was a binding extradition treaty between India and Chile.
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The woman had contended there was no valid extradition treaty between the two countries.
She was arrested on February 16, 2015, from Uttar Pradesh on the basis of a red corner notice issued against her.
Seeking the relief, senior advocate Meet Malhotra and advocate Ramni Taneja, appearing for the woman, claimed she was languishing in jail for 16 months and was a "victim of political vendetta orchestrated by the government of Chile".
The court noted in its order that the French embassy had in a note verbale sent to the Indian government sought release of the woman on humanitarian grounds.
It also noted that the French embassy in another note verbale to the government had said that it has no objection if Verhoeven's passport is seized to prevent her from leaving the country.