A video of Suzethe Margaret entering a mosque wearing shoes before letting her dog run around went viral in July.
It sparked anger in the Muslim-majority country where many consider dogs to be impure.
A panel of judges in Bogor, a town near Jakarta, found her guilty of blasphemy on Wednesday but said she could not be held responsible for her actions.
Margaret has paranoid schizophrenia, according to psychiatric examinations in 2013.
Prosecutors had demanded she be sentenced to eight months of imprisonment.