Ambulances were called to the scene at inner-city Camperdown about 8.30am, when paramedics found a 22-year-old man with stab wounds.
Police were told the alleged attacker got on a bus at nearby Parramatta Rd not long after the incident.
A short time later, the 14-year-old was arrested near Royal Prince Alfred Hospital, which neighbours the university.
NSW Police forensic investigators at the scene of an alleged stabbing at the University of Sydney. (Dan Himbrechts/AAP PHOTOS)
The injured man was taken to the same hospital in a stable condition.
In an email to students, vice-chancellor Mark Scott confirmed 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.
The teen, who police said did not know the man before the stabbing, was being questioned by investigators after his arrest.
Police tape blocking the university's Western Ave exit was taken down early on Tuesday afternoon.
A Sydney University spokeswoman earlier said staff were working with authorities and there might be an increased security and police presence on campus while investigations continue.
Students were notified a number of buildings at the university have been placed in "secure mode" and will 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.
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