Andre Gagnon was cleared of the charge at a court martial in Quebec City last month.
The 48-year-old had pleaded not guilty to assaulting then-corporal Stephanie Raymond in a military facility after a heavy drinking session at a holiday party in December 2011.
While both Gagnon and Raymond acknowledged the sex acts, the trial evolved around the issue of consent when it was presented to the all-male jury of five soldiers.
The defence argued that Raymond consented to the sex or had at least behaved in such a way that Gagnon had a "sincere" but "erroneous" belief she had agreed to it.
The prosecution service is arguing that the court martial judge erred in law when he allowed the jury to consider that defence.
The Crown alleged at the trial that Raymond was in a position of vulnerability and felt forced to submit to the advances of a superior officer.
Marylene Trudel, one of the prosecutors, indicated there would be no further comment on the appeal.
Raymond made it clear at the court martial that she wanted her name made public.