Foles told reporters he will undergo surgery Monday.
"It's not the way you want to start your time here," Foles said. "It's unfortunate, but at the same time I'm going to stay positive and trust the good Lord in this time. ... I'm still grateful I get to be a part of this team.
"I'll have surgery [Monday] to get this thing rolling and trust the good Lord for healing. I'll be ready to roll when I am."
Foles sustained the injury when Chiefs defensive lineman Chris Jones drove him into the ground on a tackle after he released the ball on a pass. The play resulted in a 35-yard touchdown to receiver DJ Chark.
After the play, Foles headed to the locker room while favoring his non-throwing arm. He later appeared on the Jaguars' sideline in a sling.
Before exiting the game, Foles was 5-for-8 for 75 yards and one touchdown with a quarterback rating of 132.8.
"It was unfortunate," Marrone said. "You'd really like to see how the game would've worked itself out with Nick."
Rookie quarterback Gardner Minshew out of Washington State took over for Foles. He completed 22-of-25 passes for 275 yards, two touchdowns and an interception.
"I was really proud of him stepping up and I'm going to be here to help him anyway possible," Foles said.