People.com said the elder Panettiere, reportedly known as Skip, was released from police custody Monday afternoon after posting $50,000 bail.
He had been arrested early Monday morning for allegedly hitting the actress' mother in the family's West Hollywood home during an argument, the entertainment news Web site reported.
Panettiere told the TV program "Extra" the episode was "a misunderstanding."
He and his wife, Lesley, also told "Extra" host Mario Lopez, "Nothing actually happened."
"In fact, Lesley wasn't even aware that Skip had been arrested," Lopez reported. "Hayden found out about her dad's arrest when he called her from jail. They love each other very much and want everyone to know that the matter was completely blown out of proportion."