Chanting mobs were reported in the capital, Dhaka, the southeastern port city of Chittagong and Bhola, Gulf News reported.
Home Minister Mohiuddin Khan Alamgir told a news conference the demonstrations aimed at disrupting traffic were actually an affront to Islam.
"The strike exposed people to misery and actually made the religion look bad," Alamgir said.
The Bangladesh government spoke out against the film, "Innocence of Muslims," and blocked online access to the YouTube site where a trailer for it is posted, but the protesters allege that wasn't enough, the report said.
Prime Minister Shaikh Hasina announced he had made an appeal to the United States to pursue legal proceedings against the filmmaker.
"No Muslim can tolerate such defamation of the Prophet," he said.
The video clip was first posted online in early July, but violent protests in Muslim countries began in earnest on the Sept. 11 anniversary of the 2001 al-Qaida terror attacks on the United States.
2014: The Year in Music [PHOTOS]