"A 28-year-old male Northern Territory police officer has been granted bail in an out-of-session Local Court hearing to appear in Alice Springs on December 19, 2019," the statement said.
"The officer has been suspended on pay.
"As this matter is before the court, no further information will be released."
According to 7News, on Saturday night Mr Walker was shot by the police officer in the remote Northern Territory community of Yuendumu.
Mr Walker wasn't able to receive medical attention as there was no medical help in the community, which is located 266 kilometres north-west of Alice Springs.
According to the police, two officers entered a residence in the community at 7:15 pm to arrest Walker for alleged property and assault offences.
There was an altercation between Walker and the officers.
Constable Zachary Rolfe shot Mr Walker.
Mr Walker was not taken to a medical facility, instead, he was taken to the police station where he died a short time later.
Family members were notified on Sunday.
There has been widespread outrage both in the Yuendumu community and across Australia after the fatal shooting of Mr Walker.
The community is now calling for an independent investigation into Walker's death, and raising pertinent questions such as why the police didn't use non-lethal tasers to subdue Mr Walker, why the medical centre was closed on Saturday night, and why no family members were allowed to enter the police station.
Warlpiri elder, Eddie Robertson, told the ABC the community was in mourning: "Today we are still crying and we don’t believe that we lost a young bloke in our town. The whole community is in mourning, even the kardiya [white] staff are in mourning, and we are standing together strongly."
On Wednesday, mass people left work early across Australia to protest, using the hashtag #istandwithyuendumu.
While the protest was incredible, our support shouldn't end there. We call on everyone - especially non-indigenous people - to rally around a community in mourning, in search of justice.
This is a developing story, more to come.