Salt Lake County Jail documents say the woman posted on Saturday that she and her son would be "dead by morning" if they were not rescued. That prompted a welfare check at the home by Sandy police.
Officers arrested 33-year-old Troy Reed Critchfield and booked him into jail for investigation of aggravated kidnapping, forcible sodomy, aggravated assault, domestic violence, child abuse, animal cruelty and other charges.
He remained in jail on Monday.
It was not immediately clear whether Critchfield had an attorney.
Police say the woman hid in a closet and used a laptop to post the Facebook message.