Mr Freeman died in Canberra's Alexander Maconochie Centre on May 27, almost one year after he was bashed into a coma in the same jail.
On Thursday, ACT's Justice Minister Shane Rattenbury announced there will be an independent inquiry into Mr Freeman's treatment in custody.
"We're undertaking this inquiry in some respects, because of Mr Freeman's Indigeneity," Mr Rattenbury told media.
“It highlights a particular sensitivity around that death, and that that's something I'm very mindful of. And it's particularly why we're moving so quickly on this matter.”
The inquiry will examine whether Mr Freeman was adequately cared for by corrections staff prior to his death last week, including whether ACT Corrective Services’ systems operated effectively and in compliance with human rights obligations.
A statement from Mr Rattenbury's office says the inquiry cannot "inquire into or consider the manner and cause of the death" of Mr Freeman "as that will be addressed by the police investigation and the Coroner".
The review will be undertaken by Phillip Moss, the former integrity commissioner who conducted a review into sexual abuse in Australia's detention centre on Nauru.
While no charges were laid after Mr Freeman's near-fatal attack in the jail last year, Mr Rattenbury says that incident can be examined within the scope of this new inquiry.
The circumstances of Mr Freeman's death have not yet been revealed.
Mr Rattenbury says he is "mindful of the effect this death in custody may have on other detainees."
He says ACT Corrective Services is working with the Indigenous Chaplaincy Service to arrange a culturally appropriate memorial service for Mr Freeman.
The inquiry is expected to be completed and a report provided to Mr Rattenbury by August 31.
You can read the terms of reference for the inquiry into the treatment of Mr Freeman here.
NITV has chosen to withhold Mr Freeman's first name.