The situation was under control Sunday afternoon after extra security officers were deployed and the government banned public gatherings in the troubled areas near the southern border with Myanmar, said Nojibul Islam, a police chief in the coastal district of Cox's Bazar.
He said at least 20 people were injured in the attacks that started late Saturday after a photo of a burned copy of the Muslim holy book was posted on Facebook. The rioters blamed the photo on a local Buddhist boy, though it was not immediately clear if he actually posted the photo.
Bangladesh's popular English-language Daily Star newspaper quoted the boy as saying that the photo was mistakenly tagged on his Facebook profile. The newspaper reported that soon after the violence started, the boy's Facebook account was closed and police escorted him and his mother to safety.
Joinul Bari, chief government administrator in Cox's Bazar district, said authorities detained the boy's parents and were investigating.
Buddhists make up less than 1 percent of Muslim-majority Bangladesh's 150 million people.
The Bangladeshi violence follows protests that erupted in Muslim countries over the past month after a low-budget film, "Innocence of Muslims," produced by a U.S.
Some two dozen demonstrators have been killed in protests that attacked symbols of U.S. and the West, including diplomatic compounds.