The violence prompted the Foreign Ministry to issue instructions to Myanmar embassies in Islamic nations, including Indonesia, to protect the lives and property of Myanmar citizens abroad.
The Foreign Ministry has also received reports of violence suffered by Myanmar citizens in Malaysia.
Witnesses said that the flashpoint for the fight in the Indonesian detention centre early on Friday was a heated argument between a Bengali Muslim cleric and a fisherman about the sectarian violence that erupted last month in central Myanmar, Sumatra police chief Endro Kiswanto said.
The Indonesian authorities are questioning 25 Bengali Muslims they suspect of instigating the violence. Three other Myanmar citizens escaped from the fight unharmed and are being kept under tight security.
Myanmar has demanded that the Indonesian government focuses on the security of Myanmar citizens under its jurisdiction by explaining the cause of the clash, investigating how knives and other weapons were available to those involved, and punishing the guilty.