Officers were called to the hospital just after midnight following reports of an alleged assault at the hospital's adult mental health unit.
An ACT police spokesman said the incident led to the death of a 38-year-old male patient.
Police then charged the 18-year-old Canberra man, also a patient, and took him to the ACT watch house.
He will appear before the ACT Magistrates Court charged with murder on Monday.
Mental health unit staff tried to revive the 38-year-old man at the scene following the assault but were unsuccessful.
ACT police detective superintendent Hall O'Meagher said officers were investigating the circumstances that led to the death of the 38-year-old.
He said no weapons were used in the incident.
"There will be a post-mortem examination in the coming days, and we're hoping that that will help us to confirm what the cause and manner of death were," he told reporters in Canberra on Sunday.
"The two people weren't known to each other on a long-term basis but they had known each other within the mental health unit over the past few days."
No other patients or staff members in the unit were injured in the incident.
"When police arrived, the situation was in control, the security staff at the hospital had got the situation under control and it was a matter of them handing it over to us at that point in time," Detective Superintendent O'Meagher said.
ACT Mental Health Minister Emma Davidson said her thoughts were with the family of the 38-year-old.
"This is a very distressing situation for families of those involved and for staff and other patients at the adult mental health unit," she said in a statement.
"These sorts of incidents are also felt deeply by the health services staff who are extremely dedicated to caring for their patients, and I know many will be struggling with this news today."
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