APHR said the ruling could embolden religious hard-liners in the country and called into further question Indonesia's harsh Blasphemy Law, which permits prison sentences of up to five years for those found guilty.
Indonesia has the largest population of Muslims in the world - about 85 percent.
After the verdict, the governor was taken to a Jakarta prison but it was unclear whether he would remain in jail or be released later to allow him to file his appeal.
Hard-line Islamic groups have attracted hundreds of thousands to anti-Ahok protests in Jakarta, shaking the government of President Joko "Jokowi" Widodo and undermining Indonesia's reputation for practicing a moderate form of Islam.
The five-judge panel said Gov. Basuki "Ahok" Tjahaja Purnama was "convincingly proven guilty of blasphemy" and ordered his arrest.
Ahok, who will appeal his sentence, lost the election last month to a Muslim rival and will hand over his office in October.
But Ahok supporter Adrian Sianturi said the trial was a victory for intolerance and corruption.
Hardline Islamist groups initiated the process, accusing Ahok of insulting the Quran during his losing reelection bid previous year and called for him to be arrested and tried.
The lead judge, Dwiarso Budi Santiarto, said the trial was a purely criminal one and the court disagreed that there were political aspects to the case.
On the day of the election, the Jakarta Post editorial board described the campaign as the "dirtiest, most polarizing and divisive" ever seen in Indonesia.
At least several thousand white-robed protesters marched after Friday prayers at Istiqlal Mosque in central Jakarta until reaching the nearby Supreme Court building.
Tobias Basuki, an analyst from Jakarta think-tank the Centre for Strategic and International Studies, said the shock decision could have been driven by pressure from Purnama's political foes on the notoriously corrupt judiciary to remove the governor from power as soon as possible.
The controversy began in September when the governor, known for his outspoken style, offended Muslims by mockingly quoting a passage from the Qur'an during his reelection campaign.
Ahok was charged with blasphemy after he said that clerics were misleading voters by telling them that Muslims were not allowed to vote for a Christian.
An incorrectly subtitled video of his comments later went viral, helping spark huge demonstrations that ultimately resulted in him being bought to trial. The legislation was rarely used during the 32-year rule of strongman Suharto, but in recent years it has been exploited to persecute minorities, rights groups say.