This detention center does house convicted IS militants but Indonesian police are yet to provide any information on the background of the rebellious attackers.
"There have been six fatalities - five of our comrades are dead and one of them also (died)", said national police spokesman Muhammad Iqbal.
In a message carried on its Amaq news agency, the Islamic State group (IS) claimed responsibility for the incident and said 10 counter-terrorism officers had been killed. The country is embroiled in an ongoing armed struggle with Islamic State. "We can not be rash because it involves national security", Wiranto explained.
The riot broke out late on Tuesday in the prison, located in Depok and holding suspected members of the Islamic State of Iraq and the Levant (ISIL) group.
Iqbal said an inmate was fatally shot after grabbing weapons and threatening officers.
"If they surrender, it will be a non-violent process".
Mr Iqbal said a dispute had broken out with prisoners who objected to authorities making checks on food being brought into them. "But if there is a threat to officers or others, we will take very strong action", he said, adding that the hostage was reported to be safe and the officers' bodies have been transferred to a nearby hospital.
The incident was triggered by the objection of the prisoners' requirements on food, the spokesman said.
Police officers maintained tight security around the jail on Wednesday (local time) and kept onlookers away from the entrance.
The world's most populous Muslim nation Indonesia has carried a lot of crackdown on militants since Bali bombing in 2002.
In January 2016, four Islamic State-linked militants mounted a gun-and-bomb attack at an intersection outside a Starbucks cafe in central Jakarta, killing themselves and four others.