Homosexuality is not outlawed in Indonesia except in conservative Aceh province, which adheres to strict Islamic laws.
But gay couples often face persecution and discrimination in the world’s most populous Muslim-majority country, where homosexuality remains taboo.
Anwar Abbas, deputy chairman of the Indonesian Ulema Council, Indonesia’s most powerful Islamic regulatory body, criticised the decision to go on with the show.
“We know that Coldplay supports LGBT, but now the question is, is the LGBT behaviour in line with … our constitution?” he said in a statement on Wednesday.
“There are six religions recognised in this country, and not one of them allows and tolerates LGBT practice.”
Jakarta police spokesman Trunoyudo Wisnu Andiko told reporters the protesters did not have a permit to stage a rally.
The police deployed nearly 4,000 officers to secure the sold-out concert.
The band has not commented on the protests but it posted an image of lead singer Chris Martin walking barefoot through central Jakarta on Tuesday.