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.

The car's owner came out of Aldi in Gorton, Manchester on Monday, as a man allegedly forced his wife and son, 5, out of the car and tried to drive off.
As the vehicle reversed, owner Tahir Mehmood jumped in the passenger seat. The car crashed into another vehicle when the alleged car thief ran off.
Kyle Jones, 23, of Cheadle Street, Openshaw is due in court later.
He will appear before Manchester Magistrates' Court charged with attempted robbery and possession of an offensive weapon.

Mokhtar Belmokhtar was killed in the eastern city of Ajdabiya, a statement from Libya's government said.
The US says Belmokhtar was targeted and the strike was successful, but it is assessing the operation's results and would give details "as appropriate".
Mokhtar Belmokhtar's death has been reported many times in the past.
Born in Algeria, Belmokhtar was a former senior figure in al-Qaeda in the Islamic Maghreb (AQIM), but left to form his own militia.
He gained notoriety with the attack on the In Amenas gas plant in Algeria in 2013, when about 800 people were taken hostage and 40 killed, most of them foreigners, including six Britons and three Americans.
The US has filed terror charges against him and officials said they believed he remained a threat to Western interests.
"Belmokhtar has a long history of leading terrorist activities as a member of AQIM, is the operational leader of the al-Qaeda-associated al-Murabitoun organisation in north-west Africa, and maintains his personal allegiance to al-Qaeda," said Pentagon spokesman Col Steve Warren.
The Libyan government said the strike came after consultation with the US. Their statement said it resulted in the death of the "terrorist Belmokhtar".
Libya has been in chaos since the ousting of Muammar Gaddafi in 2011.
Its internationally recognised parliament is operating in exile in the eastern port of Tobruk.
A rival parliament, the Islamist-dominated General National Congress, is nearly 1,000km (620 miles) to the west in Tripoli.
Rival militia have been battling to fill the power vacuum, with Islamic State militants battling other Islamists in the east.
There has been uproar in the Indian parliament over a former Supreme Court judge's allegations of corruption in the judiciary.
[NEXT_CONCEPT]
A man has been charged after an attempted carjacking at a supermarket car park in Manchester.
[NEXT_CONCEPT]
A top Islamist militant who ordered a deadly attack on an Algerian gas plant two years ago has been killed in a US air strike in Libya, officials say.