Schwarzenegger split from his wife of 25 years Maria Shriver earlier this month, after admitting to fathering a secret love child with a member of his household staff.
Palin has described Schwarzenegger's behaviour as "disgusting", and said that the Terminator star's actions are reflective of his personality.
"i feel so bad for his children," Palin said, during an interview on Fox Business. "It must be quite embarrassing for them."
"You know, it's an irresponsible, and really a pretty disgusting thing that he did, pretty much denying that he had a child for ten years," she continued.
"That's how I look at it. It speaks to his character. It's sad."
CNN also notes that Schwarzenegger's son Patrick recently changed his screen name on Twitter from Patrick Schwarzenegger to Patrick Shriver.
Schwarzenegger recently announced that he has put all future film projects on hold on hold while he deals with his family issues.