Senior police officers in the Cox's Bazar coastal district said deployments of soldiers and border guards had helped quell the violence.
A young man accused of posting the photo was escorted to safety. At least 20 people were said to have been injured. Public gatherings had been temporarily banned, police said.
The rioters' targets were the town of Ramu and its adjourning villages, some 350 kilometers (216 miles) from the capital, Dhaka.
"They became unruly and attacked Buddhist houses, torching and damaging their temples from midnight to Sunday morning," said district administrator Joinul Bari.
A police officer, Rumia Khatun, said thousands of Muslims first attacked a Buddhist hamlet in Ramu, torching centuries-old temples, and later stormed Buddhist villages outside the town.
A local journalist, Sunil Barua, himself a Buddhist, said two of the temples set ablaze during the rioting were 300 years old.
"They looted precious items and Buddha statues from the temples. Shops owned by Buddhists were also looted," Barua said.
The Muslim head of the local council, Sohel Sarwar Kajal, said he was trying to mediate.
"We are doing everything possible to quell tension and restore peace between the communities," he said.
Buddhists make up less than one percent of Bangladesh's 153-million population and reside mainly in southeastern districts, close to the border with Buddhist-majority Myanmar.
Sectarian tensions have been running high in Myanmar since June when deadly clashes erupted between Buddhists and minority Muslim Rohingya in Myanmar's western Rakhine state.
ipj/tj (Reuters, AFP, AP)