Morrison quit after meeting with station executives, the New York Daily News reported.
Morrison, 44, was arrested after he allegedly choked and threatened to kill his wife, CBS MoneyWatch reporter Ashley Morrison, during a late-night fight at their home in Darien, Conn.
"My family is my first and only priority right now and I have informed CBS management that I need to put all of my time and energy into making sure that I do what's best for my wife and my son," Rob Morrison said in a statement. "I very much appreciate the opportunity that CBS has given me and I thank them for accepting my decision."
TV station executives had no comment on Morrison's situation.
The Morrisons have been together for five years.
Rob Morrison, who is free on $100,000 bond, denies threatening his wife, who police said had red marks on her neck.
He said the argument started over watching the romantic comedy "Mystic Pizza" and that he sustained a broken nose in the fracas. The Stamford Advocated reported the dispute was over Facebook photos.
A police source told the Daily news Ashley Morrison had called New York police seven times about her husband's allegedly abusive behavior between 2003 and 2009.
Morrison, an ex-Marine, could be sent to prison for as much as five years in prison if convicted.