The ruling was made last year but only came to light this week.
Mario Tolosa, a sports club official, was originally given a six-year sentence, but the judges halved it.
Among the arguments they used to justify this was a claim that the boy showed signs of transvestite conduct.
Interior Minister Florencio Randazzo said the ruling was "an embarrassment".
He said: "It's repugnant to say that the presumed sexual orientation of an abused six-year-old boy is a reason to reduce the sentence of the abuser.".
President Cristina Fernandez de Kirchner's cabinet chief, Anibal Fernandez, said judges Horacio Piombo and Benjamin Sal Llargues should be "hauled before an impeachment hearing".
He said the country was "in the hands of morons" and that it was "one of the biggest disgraces we've ever seen in this country".
Tolosa had been vice-president of a neighbourhood football club in Buenos Aires.
He was convicted of abusing the boy in the club's bathrooms in 2011.
On Monday, Judge Piombo defended the ruling in interviews on TV and radio.
He said that the child had already been abused before Mario Tolosa had attacked him, being initiated by his father into the "worst of worlds, leading him to deprivation".
As a result of that experience with the father, the child had showed "signs of transvestite conduct, of conduct we had to take into account", he added.
Judge Piombo said the ruling had been leaked in a attempt to discredit him and his colleague.
The family of the boy say they will appeal to the Supreme Court.
Speaking to La Nacion newspaper, the boy's aunt said the child's father had been in prison for rape for much of his son's life and his mother had disappeared, leaving her child with relatives.
She said the judges had not understood that, although he had come from a poor and troubled family, he had not previously been abused.
Under Argentine law, "simple abuse" is punishable by three to 20 years in prison.
Harsher sentences are imposed for "aggravated abuse" which Mario Tolosa was originally convicted of.
Two Argentine judges are facing calls for their impeachment after reducing the sentence of a paedophile on the grounds that his six-year-old victim had been abused before.