"We need everybody to be praying for his family and this officer," Sheriff Wayne Coats said Monday.
James Eric Cook has more than 10 years of service with the department.
Authorities say he was shot Saturday by 16-year-old Mario Alexander Garza III.
Garza was the subject of a missing persons report on Friday. Cook was following up with the investigation of the missing persons report when he encountered Garza and a scuffle broke out.
Officials said Monday that Cook is stable.
"It was a sickening phone call that I got," said Sheriff Coats. "When they said he had been shot, I knew officer Cook always wore a vest and I thought if he wasn't hit anywhere else he'll probably be okay. On the way to Cape Fear I got the phone call that he had been shot in the face."
Garza was also arrested in February after bringing a pocket knife to school.
He's now charged with attempted murder, assault with a deadly weapon and assault with a firearm on law enforcement.