The court overruled a November ruling by the Satakunta district court, which found Anneli Auer guilty of killing her husband in the town of Ulvila in December 2006. She was sentenced to life in prison.
The verdict has been expected since late May when the court freed Auer pending the ruling on her appeal.
On Friday the appeals court said that there was not sufficient evidence to prove that she murdered her husband and that her professions of innocence seemed genuine.
It added that it was unlikely that Auer would have had enough time between calling emergency services and their arrival to stage the crime scene to suggest that an intruder carried out the killing.
She has unswervingly denied all charges.
The prosecution has 60 days to appeal to the Supreme Court.