Murdoch is a force in the conservative world, where Fox News Channel has profoundly influenced television and US politics since its start in 1996.
Even worse for the network, Trump has talked of appearing in an online interview with former Fox star Tucker Carlson at the same time.
In her federal lawsuit, Grossberg asserted that Carlson's show had a cruel and misogynistic workplace and that she had been pressured to give misleading testimony during the Dominion case trial.
The producer, Alex McCaskill, confirmed his exit in an Instagram post. He had remained at Fox after Carlson, the network’s most popular personality, was fired on April 24.