A number of prisoners escaped, he said, but seven have since been recaptured.
Citing an initial report, Mr Somsak said the protest began about 11.45am in the dining hall while warders were busy refurbishing an isolation cell for inmates infected with communicable diseases.
About 100 inmates, some of them facing a life sentence, set fire to the dining hall and demolished the visiting room for relatives.
Thick smoke was seen billowing from the prison into the sky.
“The fact is that none of the prisoners in Buri Ram were infected [with the coronavirus] - they only started this rumour to find supporters,” the minister said, adding the cafeteria and visiting areas were among the areas torched.
Mental health workers were later deployed to reassure prisoners “after some rumours were spread” about a COVID-19 outbreak, deputy Provincial Police Region 3 chief Pol Maj Gen Akkaradej Pimonsri said.
“The situation is under control,” he added.
A number of the protesters escaped during the riot. Although the exact number is yet to be confirmed, local police said they are hunting at least six inmates known to be on the run.
The breakout prompted prison officials to alert the governor and ask police and military personnel to set up checkpoints to intercept the escapees.
Mr Somsak said he was last notified that seven of the escapees had been recaptured while inmates who were not involved in the riot had been confined to their quarters for the time being.
He said Pol Col Naras Savestanan, director-general of the Corrections Department, had travelled to Buri Ram to investigate.
Pol Col Naras, in a media interview on a helicopter flight to Buri Ram, said five people were initially reported hurt in the incident but details were still emerging.
The situation was under control but details were not yet clear, he added.
Buri Ram Prison, like other prisons nationwide, has been closed to visitors to stem the coronavirus outbreak under the government’s executive decree for administration in emergency situations.