The violence took place in Borhanuddin in the southern district of Bhola when angry protesters demanded the punishment of a Hindu man for the alleged Facebook comment, said local police chief Sarkar Mohammad Kaisar. The man denied making the comment, saying his Facebook account had been hacked.
Kaisar said four people were killed and the injured, including about a dozen police officials, were being treated in local hospitals. Bangladesh's leading newspapers said about 100 people were injured.
Bhola is 72 miles (116 kilometers) south of the capital, Dhaka.
Local authorities held a meeting Sunday to try to defuse the tensions that began Friday as the Facebook post gained attention in the area. But the angry protesters started attacking security officials, prompting them to retaliate, Kaisar said.