A man has been arrested after he allegedly drove a ute towards a woman holding an 11-month-old-baby in Alice Springs, narrowly missing them, in what police have described as "a domestic violence incident".

Northern Territory police allege the 32-year-old man physically assaulted his partner while she was holding the child at about 1:20am on Monday, while inside a ute stopped outside a 24-hour convenience store on Todd Street.

When the woman left the vehicle with the baby and walked towards the shop, the man allegedly drove towards the pair, narrowly missing them, and crashed into the shop entrance.

Police said the baby was unharmed, but the woman was taken to hospital with non-life-threatening injuries.

The man fled the scene, but was arrested by police on the Stuart Highway, south of

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