The freedom of religion report followed a fact-finding visit by CSW to Indonesia in May 2017, shortly after the verdict was delivered in the blasphemy trial of the former governor of Jakarta.
Basuki Tjahaja Purnama, also known as Ahok, is a double minority as an ethnic Chinese Indonesian and a Christian. He was falsely charged with blasphemy during his re-election campaign.
The Christian charity has recommended to the Indonesian government to repeal blasphemy laws and to extend human rights education.
Representatives of CSW met with religious communities and civil society in Jakarta, West Java, Central Java and North Sumatra, including representatives from the Ahmadiyya and Christian communities, and Parmalim traditional religion.
Concerns raised included social hostility, the closure of places of worship, harassment and threats of violence toward religious minorities.
Benedict Rogers, CSW's East Asia Team Leader said: "The rise of religious intolerance and the climate of fear among religious minorities was palpable, and the tension in Indonesia following the imprisonment of Ahok was obvious."
According to CSW, Indonesia is a Muslim-majority nation and has a tradition of religious pluralism and prides itself on its reputation as a role-model of a moderate, tolerant and democratic Muslim-majority nation that protects freedom of religion or belief.
However, the report found this reputation "is being seriously undermined" by the rise of radical Islamism and its influence on politics and society in the country.
A representative of the Ahmadiyya community said: "Tell the world the truth. Our hope is that you remind the government of Indonesia that Indonesia is not an Islamic country.
"Remind our government that it is not a religious government. Remind our government to protect tolerance and pluralism as the basis for Indonesia. Our country is multi-ethnic and multi-religious."