The boy allegedly stabbed a 22-year-old man at the inner-city Camperdown campus about 8.30am on Tuesday with paramedics treating him at the scene before rushing him to Royal Prince Alfred Hospital.
The campus went into lockdown as police raced to the scene and searched for the attacker.
The 14-year-old is alleged to have caught a bus to Royal Prince Alfred Hospital where he was arrested.
NSW Police Assistant Commissioner Mark Walton said the stabbing was being treated as a terrorist incident.
NSW Police forensic investigators at the scene of an alleged stabbing at the University of Sydney. (Dan Himbrechts/AAP PHOTOS)
However, investigators had not identified a particular ideology and had ruled out religion as a factor.
The 14-year-old boy was previously known to both police and government agencies, Mr Walton said.
The boy was treated for cuts at the hospital and was undergoing a mental health assessment.
Police said the victim was in a stable but serious condition.
Forensic officers have been scouring the campus grounds looking for the weapon and other evidence that could assist in the case.
Forensic officers searching the university campus carry away evidence in brown bags. (Dan Himbrechts/AAP PHOTOS)
In an email to staff and students, vice-chancellor Mark Scott said he was "shocked and saddened" by the attack on a member of the university community in what he described as an isolated incident.
"NSW Police have arrested the alleged attacker and have assured us that there is no ongoing threat to the community," he wrote.
A Sydney University spokeswoman said staff were working with authorities and that there might be an increased security and police presence on campus while investigations continued.
Students were notified a number of buildings at the university had been placed in "secure mode" and would require swipe cards for access.
University international cardiology fellow Matheus Silva said he was concerned by news of the stabbing after moving away from his home country to escape violence.
"One of the main reasons I left Brazil was because of the criminality," he told AAP.