Sheridan leaves the club after they lost one and drew two of their first three games of the season back in League Two.
The former Republic of Ireland international becomes the second boss to lose their job this term already, following Andy Thorn's departure from Coventry City at the weekend.
Tommy 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."
Sheridan led the Spireites up into League One with a title-winning 86 points in 2011, an achievement which saw him named League Two Manager of the Year by the League Managers' Association.
The former Leeds United and 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.
However, they were not able to avoid relegation from League One, losing six of their final 10 games of the campaign as they finished the campaign eight points from safety.