Police described the stabbing scene as chaotic as parishioners screamed as the attack unfolded.
The choir's pianist, Brenda Baca King, told KRQE-TV that the attacker was looking at the lead soloist. "I just remember seeing him hurdle over the pews, hurdle over people and run (toward) us and I thought, 'Oh my God, this is not good,'" Baca King said.
Capener was interviewed by police and was expected to face felony charges, Gibbs said.
It's not yet known whether Capener has an attorney.
Archbishop of Santa Fe Michael Sheehan released a statement Sunday afternoon saying he was saddened by the attack.
"This is the first time in my 30 years serving as archbishop in the Archdiocese of Santa Fe and as Bishop of Lubbock, that anything like this has occurred," Sheehan said. "I pray for all who have been harmed, their families, the parishioners and that nothing like this will ever happen again," Sheehan said.
The church didn't immediately return calls seeking comment on Sunday afternoon.
Follow Russell Contreras on Twitter at http://twitter.com/russcontreras