Mark, who this year recorded his first country music album, is frequently seen wearing the hat.
He chalked up the other man's behaviour to drinking.
"Sometimes men do silly things," Mark said.
NZ First leader Winston Peters had a few choice words about the situation.
"I'd do something about it if he'd stolen my hat," Peters told Newshub.
"I'd make sure he didn't feel like stealing another hat for a long time, that's what I'd do."
Earlier this year, NZ First MP Clayton Mitchell was reportedly thrown out of a bar after failing to get out of the way of bar staff.
Mitchell said he was escorted from the bar following a misunderstanding.