The Spireites are without a win so far this season as they aim for an immediate return to League One following their relegation last term.
Sheridan joined the club at the start of the 2009/10 season and won promotion the following year.
The former Sheffield Wednesday midfielder led the Spireites to victory in the Johnstone's Paint Trophy at Wembley last season - the first time the club had won the competition in their history.
But he was unable to stop their slide into the Football League's basement division and the club relieved him of his duties following a slow start.
The Spireites have named Tommy Wright as caretaker manager.
Wright, who was Sheridan's assistant, will take charge of the first team and will be assisted by former Nottingham Forest goalkeeper Mark Crossley.
Chesterfield chief executive Chris Turner told the club's official website: "Tommy will take charge of the first team for the foreseeable future.
"We need to take stock of the situation so we are not looking to make an immediate appointment.
"The board would like to thank John for the hard work he has put in over the last three years and wish him well for the future."
Wright arrived at the club with Sheridan at the start of the 2009/10 season after performing the same role at Oldham.
