The victim was found by a passerby in a parking lot near the campus tennis courts on Humboldt Street between 11th and 12th streets around 9:40 a.m., according to Sgt. John Laws.
Paramedics attempted to revive the victim before determining they were dead at the scene.
San Jose police initially responded, but then determined the homicide was within the jurisdiction of university police, Laws said.
Laws said the death is considered a homicide, but did not have any information on the likely cause of death. It is also unclear whether the homicide occurred at the location the body was found or elsewhere in the city, he said.
"We're pretty sure it had little or nothing to do with the university," Laws said.
The homicide is San Jose's 37th this year. It is only the fourth ever investigated by university police, according to Laws.