Emergency services were alerted to the incident at around 2.45pm local time on Monday.
A third person, a 34-year-old man, suffered minor injuries and was treated at the scene.
"There has been an incident on campus. Police are at the scene and have the situation under control, with an individual in custody," the ANU said in a post on X, formerly known as Twitter.
Students and staff were urged to stay away from Fellows Oval.
"Ellery Crescent near the RSSS Building is closed," the university added.
"Two 20-year-old female students have been transported to hospital, one in a critical condition and one in a stable condition," ACT (Australian Capital Territory) Policing, said in a statement.
"A 24-year-old male, who is not believed to be a student of the university, is in police custody. He has not been charged at this time.
"No other people are being sought by police."
The motive for the attack is unknown, the police force added.