Jefferson Lewis, 47, had to be airlifted to Darwin after an angry crowd attacked him then tried to storm an Alice Springs hospital on Thursday night, where he was taken following his arrest.
He is expected to be charged with the murder of the five-year-old girl, referred to as Kumanjayi Little Baby at her family's request and in line with cultural traditions.
Aboriginal Elder Michael Liddle said the unrest was an explosion of rage that ignored the consequences and undermined the community's united response to the girl's disappearance.
"What took place yesterday was an incident of anger that turned into violence that had no thinking about the consequence," the Alyawarre man told reporters on Friday.
"All week, the community of Alice Springs come together … searching for a little lady, a little baby that was taken by a monster, and that hard work was undone last night by some people who are very angry with the systems."
Four ambulances were taken off the road and crews went into lockdown for about five hours as the riot escalated outside Alice Springs hospital.
"If you had a bleed out or you had a heart attack in that time, you couldn't call the ambulances," Mr Liddle said.
The family of the five-year-old girl called for calm, asking people to let justice take its course.
"What has happened this week is not our way," senior Warlpiri elder and family spokesman Robin Granites said in a statement.
"Our children are precious - of course we are feeling angry and hurt at what has happened.
"It is time now for sorry business, to show respect for our family and have space for grieving and remembering."
Takeaway alcohol sales will be limited on Saturday as authorities attempt to stem further unrest.
The hunt has begun for rioters, with one woman arrested on Friday for attempting to torch a police vehicle.
Police were also looking for people they believed sheltered Lewis over recent days.
Northern Territory police said it was a minority of people who engaged in what they described as "disgraceful behaviour".
Elder Warren Williams said residents in the town were devastated and fearful.
"At the moment, I feel devastated by what happened all this week," he said.
Rumours and calls for "payback" or traditional punishment under central Australia's Aboriginal lore have surfaced following Lewis' arrest.
But Mr Liddle warned that risked inflaming the situation and distorting cultural practices.
He said the unrest was tied to deeper trauma and a lack of support for people leaving prison.
Lewis allegedly abducted the little girl just six days after being released from prison.
Despite the chaos, Mr Liddle said the town's response when the little girl went missing showed its true character.
Almost 200 people scoured tough terrain around Alice Springs for the child before a body was found on day five of the search.
"With all the sadness that Alice Springs community is enduring ... it just really shows the coming of people and the strength in the community and support," Mr Liddle said.
Lewis remains in custody and is expected to be charged with murder in the coming days.
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