The girl and her mother Laura Hinks, also known as Laura Bolt, were last seen in the suburb of Berrimah on Sunday.
Police said it was after a parental visit that Ms Hinks, 34, left an address about 1pm at Hidden Valley Road, and both disappeared.
Ms Hinks' last known address was in Moulden, but she no longer appeared to be living there.
Northern Territory Police on Saturday said they'd charged a 50-year-old woman in connection with Grace's disappearance while they continued to search for the child and her mother.
The woman was arrested at a home in Anula overnight and was charged with abducting a child under 16 and attempting to abduct a child under 16.
She was remanded in custody and will face court on Monday.
The woman was refusing to provide information to find the girl and her mother, Detective Acting Senior Sergeant Jon Beer said.
"Police will use all resources necessary to locate Grace," he said.
Grace is described as having a fair complexion with brown hair and eyes. She was last seen wearing a short-sleeved white dress, as well as white socks and black sneakers.
Her mother has a fair complexion, a slim build and dark hair and eyes.
She was last seen wearing a white and green floral-patterned ankle-length dress or skirt, with a white or cream long-sleeved shirt.
Anyone with information is urged to contact police or Crime Stoppers.
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