Charles Richard Jennings, 35 was taken into custody several hours after the shooting just before noon at St. James Catholic Church, KSTU-TV, Salt Lake City reported.
The victim, whose name had not been released, was hospitalized in critical but stable condition, Ogden police said.
"This was not a random act of violence. The suspect was specific in the desired target and action," police said in a statement.
Authorities allege Jennings shot his father-in-law in the back of the head during the church service, then held stole a man's pickup truck at gunpoint to make his getaway. The truck was found abandoned along a highway north of Ogden.
Jennings was arrested without incident about 3:40 p.m. local time in Box Elder County, the TV station said.
The Deseret News reported the arrest took place north of Tremonton on Interstate 84.
A member of the congregation told the newspaper the shooting happened as parishioners were lining up to take communion. She said the gunshot sent some worshipers diving under pews while several men chased after the shooter.
Jennings has a lengthy criminal history, including felony domestic violence and drug possession charges, the News said.
No other injuries were reported, KSTU-TV said.