Police were called to the residence in Corpus Christi on Wednesday evening and found the pastor with a chest wound.
Lt Jay Clement told local reporters that a band member was stabbed in the neck and two other people were injured trying to get the suspect away from the pastor.
The pastor and band member have been taken to hospital with life-threatening injuries.
While it is not clear what the motive behind the attack was, Clement told The Corpus Christi Caller-Times that a witness said the suspect - who has been arrested, was a parishioner.
The group had been meeting at the home each day as part of a "40-day pledge".
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