The Britain-based Syrian Observatory for Human Rights said that at least 52 people had been killed in the blasts but said the figure could rise dramatically.
As well as students, the campus houses some 30,000 people who have fled homes in areas of the city ravaged by fighting since July last year.
Video footage posted by students on the Internet showed tearful survivors taking refuge in a campus building.
Activists said missiles fired by government jets were responsible for the blasts. A military source said it was a stray surface-to-air missile fired by rebels.
The explosions struck an area near the university dormitories and the architecture faculty, the Observatory said.
State television said "terrorists launched two rockets" at the university complex, which lies in a government-controlled area of the battleground city.