The extremists were angry that the sentence was too lenient and went on the rampage, burning two churches and damaging a third, attacking the police outside the courthouse, vandalising cars, and demanding the death penalty for blasphemy charges.
The violence follows the release of a report by the Jakarta-based Setara Institute for Democracy and Peace documenting 91 violations of religious freedom in 2010. CSW said that the number of incidents affecting Christians had jumped from 12 in 2009 to 75 last year.
CSW also expressed its concern for Ahmadiyya Muslims, a religious group that considers itself to be Islamic but is shunned by many other Muslims.
The group has also experienced an upsurge in violent attacks in recent weeks. Two days before the church attacks in Central Java, a crowd of around 1,000 people attacked 20 Ahmadiyya Muslims in Cikeusik, Banten province with machetes and other weapons, killing five and seriously injuring five others.
A source warned CSW that the "inaction" and "blatant negligence" of the Indonesian government was encouraging fundamentalists to resort increasingly to extreme violence.
CSW's Advocacy Director Andrew Johnston said there had been a "dramatic" increase in the number of violent attacks against religious minorities in Indonesia in the last two years.
"Indonesia has a long tradition of pluralism, enshrined in its state philosophy, the 'Pancasila', and we urge the Indonesian authorities to defend those values," he said.
Mr Johnston urged the Indonesian government to repeal the blasphemy law and a joint decree which bars the Ahmadiyyas from promoting their beliefs.
He called for an independent investigation into the recent attacks and appealed to the Indonesian government to take action to ensure that the perpetrators are brought to justice.
"If extremists are allowed to continue to terrorise religious minorities with impunity, Indonesia's proud tradition of pluralism and religious freedom will be under threat," he said.