The violence broke out in Cox’s Bazar district when one side opened fire, killing four people at the scene, said Shihab Kaiser Khan, commander of the Armed Police Battalion, which oversees the camp’s security.
Two others died in a hospital while they were being treated for their injuries, Khan said.
Khan said one Rohingya man was detained with weapons but did not provide any further details. He said police were searching the camp for other suspects.
Friday’s violence occurred about three weeks after an international representative for the Rohingya refugees was shot to death in the camp in the same sub-district of Ukhiya.
Police have made several arrests related to his murder.
More than 700,000 Rohingya have fled to refugee camps in Bangladesh since August 2017, when the military in Buddhist-majority Myanmar began a harsh crackdown on the Muslim ethnic group following an attack by insurgents. They joined hundreds of thousands of others who have fled to Bangladesh over decades.
The 2017 crackdown included rapes, killings and the torching of thousands of homes, and was termed ethnic cleansing by global rights groups and the U.N. While Bangladesh and Myanmar have sought to arrange repatriations, the Rohingya are too fearful to return home.
Overall, Bangladesh has been sheltering more than 1.1 million Rohingya refugees from Myanmar after previous waves of persecution.