San Jose police say units responded to Grace Baptist Church near the San Jose State University campus.
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Officials first tweeted the information around 8:45 p.m. but the stabbing was first reported at 7:53 p.m.
Some victims have life-threatening injuries, police said.
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San Jose Mayor Sam Liccardo expressed his condolences on Twitter, but later had to delete the tweet due to a factual error. He then posted, "I've just deleted a tweet that made reference to the ongoing investigation into the stabbings at Grace Baptist Church this evening. A statement will be coming out shortly from SJPD regarding the status of the investigation and arrest."
SJPD is not confirming the arrest of the suspect yet.
No church services were being held at the time of the incident. SJPD say unhoused individuals were brought into the church to "get them out of the cold."
No further information has been made available.