Christopher Wenthe was working at Nativity of Our Lord Catholic Church in St. Paul in 2003 when the woman sought spiritual counseling.
A jury found him guilty last year of third-degree criminal sexual conduct.
A judge sentenced him to a year in jail, but he was released after serving eight months.
The appeals court ruled that Wenthe's conviction was unconstitutional because prosecutors obtained it "based on evidence that was excessively entangled in matters of religion."
The court said that evidence "pervaded the entire trial" and improperly shaped the verdict by giving the jury religious instead of secular standards for judging the priest's conduct.
"It invited the jury to determine appellant's guilt on the basis of his violation of Roman Catholic doctrine, his breaking of the priestly vows of celibacy, and his abuse of the spiritual authority bestowed on Roman Catholic priests; additionally, the evidence invited concern about the response of church authorities to the victim's complaint. ... The prosecutor repeatedly injected Roman Catholic doctrine and practice as a backdrop for underscoring appellant's culpability," the ruling said.
Wenthe admitted during his trial that he had a sexual relationship with the woman but denied he was still giving her spiritual counseling when their relationship turned physical in his private quarters at the church rectory in November 2003.
Their last sexual encounter was in February 2005. She reported Wenthe to church officials early that year and to police in 2010.
Wenthe remains a Catholic priest on inactive status.