The shooting was reported about 2:45 pm. at a unit in the Blossom River Apartments complex, 1000 Blossom River Way.
The victim wasn't conscious or breathing when officers arrived.
They gave him lifesaving measures and medical crews were summoned, but the man died at the scene, police said. His name was not released.
The suspect fled the scene before police arrived, officials said.
No other information about the shooting was released on Monday.
The death is San Jose's 15th homicide this year.