JAKARTA—Islamic militants based in the Middle East used bitcoin and online-payment services such as PayPal to fund terrorist activities in Indonesia, the world’s largest Muslim-majority nation, an official with the country’s financial-transactions agency said Monday.

Among the alleged donors is Bahrun Naim, a Syrian-based Indonesian who police say is involved with Islamic State and has helped coordinate attacks back home, said Kiagus Ahmad Badaruddin, chairman of the Indonesian Financial Transactions Report and Analysis Center,...