Officers identified the victim as 44-year-old Steven Christian.
They were called at about 12:30 pm Wednesday for a report of a stabbing inside a gated area at the shelter.
When they arrived, they found Christian with a stab wound to the chest.
He was rushed into surgery at Community Regional Medical Center, but died.
Police say the stabbing happened in front of several people.
Staff members chased down and detained 45-year-old Daniel Salinas, who was later identified as the suspect.
Salinas was booked into the Fresno County jail on one charge of murder.
Authorities say both Salinas and Christian were unhoused.
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