The Happy Mondays frontman, who had notoriously bad teeth before getting them repaired in 2006, praised the X Factor winner.
"I've seen quite a bit," he told The Sun when asked about the latest series of the show.
"I quite like that James Arthur kid. He's good but he should see my dentist."
Ryder also had kind words to say about X Factor alumni One Direction.
"Harry Styles and that?" he said. "Came runners-up, didn't they? Bunch of kids having a great time. Brilliant."
Arthur's first single - a cover of Shontelle's Impossible - shot to number one over the weekend.
Watch James chat to Digital Spy below: