Witnesses said angry crowds set fire to homes and temples in the Cox's Bazar district, forcing families to flee.
A curfew has been imposed and security forces are patrolling the streets.
The man accused of posting the image is in protective custody. Police say he was tagged in the photo but did not post it himself.
'Premeditated communal violence'
Buddhists in the area, in south-east Bangladesh, said their possessions were stolen before their homes were destroyed.
"Before they set fire to my home, they looted everything," said resident Sumoto Barua.
Mohiuddin Khan Alamgir visited the scene and condemned the violence
"They took our possessions, money, gold and even computers. Then they torched the house. I am now living under open sky."
The violence erupted on Saturday and continued into the early hours of Sunday.
Hundreds of protesters are said to have rampaged through Buddhist neighbourhoods, smashing statues, burning down monasteries and attacking houses.
The violence spread to the outskirts of the port city of Chittagong, where a Hindu temple was also attacked.
Bangladeshi Home Minister Mohiuddin Khan Alamgir visited the scene and described the violence as "premeditated and deliberate acts of communal violence against a minority".
District Commissioner of Cox's Bazar, Jaynul Bari, told the BBC Bengali service the government was already helping the victims.
"We have distributed food rations for them. The army will supply more food," he said.
"We are giving them building materials. The home minister has ordered that all the homes and the temples be restored to their former condition with the funds provided by the government."
The authorities have now deployed additional security to prevent further violence and a curfew has been imposed in the worst affected area of Ramu sub-district.
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