The court in the southern city of Granada, where the abuse was alleged to have taken place, ruled there was insufficient evidence against 63-year-old Roman Martinez.
It said the young man's testimony during the trial held in March had inconsistencies and contained "absolutely improbable aspects".
Martinez had been charged with "continued sexual abuse, with the introduction of a bodily member anally and attempt to introduce the penis" involving an underage boy between 2004 and 2007.
His accuser, born in 1990, would have been 14 when the alleged abuse began.
According to the court ruling he met the priest in "1998 or 1999" at a local church and became a close friend, sometimes sleeping at the parochial house where the clergyman lived.
Before turning to the courts, the young man in August 2014 sent a letter to Pope Francis describing the abuse he said he suffered at the hands of the accused and his entourage.
The letter described "constant kissing, massages and masturbation", according to the court.
Pope Francis told reporters in November 2014 that he heard of the case "with great pain, very great pain, but the truth is the truth and we should not hide it" and said he had ordered a church investigation.
After the scandal broke, the Archbishop of Granada, Francisco Javier Martinez, removed some priests linked to the case from their duties.
During a mass in November he threw himself on the cathedral floor, in front of the altar, in a gesture of apology to abuse victims.
The court had initially charged ten Catholic priests and two laymen over the affair.
But in February 2015 it dropped charges against 11 of the 12 suspects because it said legally too much time had passed between the alleged crimes and the complaints being made.
It said their accuser should have brought a case within three years of turning 18.
The lawyer for the main accuser said his client had been unable to report the crime until he had moved out of Granada.
Many survivors of abuse by priests are angry at what they see as the Vatican's failure to punish senior officials who have been accused of covering up scandals.
Prodeni, an association that defends abused children that took part in the proceedings, told AFP it could file an appeal. The Vatican has also ordered an investigation, it said.