Kirchner dismissed Redrado earlier this month because he opposed her bid to use $6.6bn in foreign currency reserves to service debt obligations this year, however, a court ordered his reinstatement a day later.
Fernandez's push to tap the reserves to help meet some $13bn in debt repayments this year has raised political tension.
Another court ruled on Friday that congress should decide whether Fernandez was right to dismiss Redrado, but government ministers interpreted the ruling as also saying he had to step down.
Fernandez said Redrado would not be allowed to continue working at the bank.
The bank's board of directors named Miguel Pesce, the bank's vice-president, as Redrado's replacement.
Pesce's appointment had already been announced before the federal court ordered Redrado's reinstatement.
Officials from both the ruling party and opposition also said the latest ruling meant Redrado should step aside, but in a letter to a leading newspaper on Sunday, Redrado pledged to remain in his post.
"I maintain my decision to continue carrying out my duties as an official unless congress says otherwise in order to comply with the law and my convictions," he wrote in the letter published in La Nacion, an Argentine daily newspaper.
A special congressional commission is due to meet on Tuesday to discuss Redrado's fate, but Fernandez has said that any recommendations it makes are non-binding.