The court martial’s jury rendered its decision on Friday after considering the matter for three days.
Gagnon, 48, faced 10 years in prison if a guilty verdict had been returned in the case, which saw the officer accused of the sexual assault of former corporal Stéphanie Raymond.
Raymond alleged that Gagnon assaulted her in December 2011 at the Régiment de la Chaudière armoury in Lévis, Quebec.
Raymond accused Gagnon of taking advantage of his position as her superior and maintained that the encounter was not consensual.
Gagnon’s lawyer, Maj. Philippe-Luc Boutin, portrayed Tremblay as calculating and manipulative and argued she knew what she was doing.
Gagnon hugged Boutin when the verdict was pronounced.
Raymond was not present for the verdict on Friday.
The prosecution now has 30 days to consider an appeal.
Prosecuting lawyer Maj. Gabriel Roy said he will assess that possibility in the coming weeks.