George Kay was charged with assault by beating and possessing a banned weapon after an alleged row at their home in Crowborough, East Sussex.
The 36-year-old, from Warrington, in Cheshire, had denied both charges following the incident last September.
Not guilty verdicts were entered when he appeared before Lewes Crown Court.
Assault charges against the estranged husband of former Atomic Kitten singer Kerry Katona have been dropped after the Crown offered no evidence.