The Blues have taken just seven points from eight games and currently sit 21st in the Vanarama National League, without a win at home since December.
They have lost two of their last three games, taking one point from fixtures against Torquay United and Solihull Moors, who are below them.
McCarthy took over as caretaker manager in 2016 and guided the club to safety with three wins in their final four games before signing a one-year contract as permanent manager.
In January this year, he signed a new two-and-a-half year contract.
A statement on the club's website said: "The Club would like to place on record their sincere thanks to Jon, a thoroughly decent man who could not have worked harder to try and deliver success – and could not have shown more commitment to the Community and the Club.
Tom Shaw, Dave Felgate and Calum McIntyre have been asked to prepare the team for the forthcoming fixtures – we ask everybody who can to get down to the Swansway Chester Stadium and get behind the staff and players this weekend as we seek to reverse our fortunes at home."