John Hennigan, 50, of Harlow, was being sentenced at Chelmsford Crown Court for his ninth breach of an anti-social behaviour order in 11 years.
He used an offensive word to describe Judge Patricia Lynch QC and she responded with the same term of abuse.
As first reported in The Guardian, the judge told investigators she "deeply regretted the incident".
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Her comment prompted a number of public complaints which were sent to the Judicial Conduct Investigations Office (JCIO) for consideration.
Judge Lynch, who was called to the bar in 1979 and appointed a circuit judge in 2014, jailed Hennigan for 18 months for insulting and making racist slurs to a black Caribbean mother in Harlow.
The QC has since "apologised unreservedly for her remarks".
She also told investigators her "remarks were a momentary lapse of judgment which should have never happened".
An investigation report sent by the JCIO to one of the complainants states: "Although the Lord Chancellor and Lord Chief Justice considered HHJ Lynch's remarks to be inappropriate, they did not find that they amounted to misconduct or warranted disciplinary action."
It added: "With the agreement of the Lord Chancellor, the Lord Chief Justice therefore advised HHJ Lynch to ensure that she responded appropriately in court at all times."
A judge who swore back at a defendant after he launched a foul-mouthed tirade at her has been cleared of misconduct.