A 52-year-old man has been charged over the alleged sexual assault of a child in Tennant Creek on Wednesday.

NT Police charged the man with "gross indecency against child under 10 years" and aggravated assault.

He has been remanded in custody and is due to appear in the Alice Springs Local Court next Wednesday.

NT Police said it opened an investigation after receiving reports on Wednesday that a witness heard a child scream and saw a man running from the scene.

Barkly MLA Steve Edgington said he had been in touch with the family of the child, who he said he understood was four years old.

"Certainly the family is shocked and devastated just like many people here in Tennant Creek regarding this alleged sexual assault," he said.

Mr Edgington said he believed the child had been taken to Alice Springs Hospital.

The incident comes nearly six years after the rape of a two-year-old child in the town.

Following that incident, then-prime minister Malcolm Turnbull travelled to Tennant Creek to announce a major funding deal to improve crises facing the town and region.