Markandey Katju said a high court judge was promoted after pressure from an ally of the former Congress government.
He also said some senior judges had made "improper compromises" in allowing the judge to continue in office.
A regional party protested in the parliament against "political interference in judicial appointments".
The Congress-led government  was in power for 10 years before losing the May general election to the Bharatiya Janata Party (BJP). The ally that Mr Katju has alluded to was the ruling party in Tamil Nadu state.
Writing in The Times of India newspaper, Mr Katju said a judge of the Madras high court in Tamil Nadu was promoted and given an extension to continue in office despite "several allegations of corruption" after pressure from an ally of the then-ruling Congress party.
Mr Katju, who is now the chairman of the Press Council of India, also told the NDTV news channel that three former chief justices of the Supreme Court made "improper compromises" in allowing the unnamed judge to continue in office.
When asked by the channel why he had waited for 10 years to make his allegations public, he said: "Concentrate on whether what I'm saying is correct or not. How does it matter if I spoke now?" Mr Katju then left the interview.
MPs belonging to Tamil Nadu's AIADMK party waved copies of the the newspaper carrying Mr Kaju's article and demanded a discussion in the upper house of the parliament.
"If you have an issue to raise, raise it through appropriate procedure. This is not the way. You are disrupting listed business," chairman of the upper house Hamid Ansari said.
The Congress party has denied the allegations and questioned their timing.
"Mr Katju wishes to remain in news. If there was any such thing then he should have spoken that time. Why he is speaking now," Congress leader Rashid Alvi said.
There has been rising public demand for greater transparency on the part of judges after allegations of corruptions against some judges over the last few years.
There has been uproar in the Indian parliament over a former Supreme Court judge's allegations of corruption in the judiciary.