At 9:06 p.m. Friday, police received reports of a disturbance involving weapons in the 1000 block of Morris Court, Sgt. Ronnie Lopez said.
Callers told police they heard a woman screaming for help and then a "pop-pop" sound, Lopez said.
Responding officers found the woman suffering from a gunshot wound and pronounced her dead at the scene.
Santa Clara police assisted in the response, and were flagged down by a witness en route to the crime scene.
The witness provided a detailed suspect description, enabling police to scour the surrounding area for the man, who was rounded up by Santa Clara police officers without incident before being turned over to San Jose police, Lopez said.
Police arrested the man, but have not yet released his identity pending the continuing investigation.
The identity of the victim, a San Jose resident, is also being withheld pending notification of next of kin, Lopez said.
The woman was the city's 16th homicide victim so far this year.
Anyone with information is asked to call San Jose police at (408) 277-8995.