Jurrah, 23, is on personal leave from the Demons, after complications during his recovery from wrist surgery.
Northern Territory police have confirmed they attended a disturbance at Little Sisters Town Camp on the outskirts of Alice Springs overnight.
"On arrival police found a 35-year-old man with serious head injuries alleged to have been inflicted by a machete," a police spokesperson said.
"Two men aged 23 years are currently in police custody with investigations continuing."
Melbourne confirmed Jurrah's arrest in a statement on its website.
"The Melbourne Football Club has been advised that Liam Jurrah, who is currently on personal leave to deal with family and community issues in Central Australia, is being held by police following an incident overnight.
"No charges have been laid."
Police have confirmed they're investigating a second stabbing in Alice Springs where a young man was found lying in a car in a car park.
A 30 year-old female is in custody for offences relating to the incident.
Superintendent Michael White said police were investigating if the incidents are linked.
