The 51-year-old Welshman was only appointed in May, but the club are 16th in the table after Saturday's 4-0 home defeat by Swindon Town.
Saunders lost 11 of his 20 league games in charge, and the Spireites are only four points above the relegation zone.
Chairman Dave Allen said: "We will not be rushed into making a decision on a new manager."
Chesterfield's last league victory was a 3-0 win over Southend on 20 October, and they have lost their last four games.
Saunders succeeded Paul Cook as Spireites manager, signing a two-year contract.
Cook had guided the Derbyshire side to the League One play-offs, where they lost to Preston, before leaving to take over at Portsmouth.
Former Wales international Saunders had previously managed Wrexham, Doncaster Rovers and Wolves, and ended last season in interim charge of Crawley Town, but was unable to stop them being relegated to League Two.

No politician from the DUP or UUP was at his funeral in St Eugene's Cathedral on Thursday.
Dr Daly became synonymous with the events of Bloody Sunday in 1972.
A spokesperson for Hilary McClintock, the mayor of Derry City and Strabane District Council, said the deputy mayor attended in her absence.
Dr Daly died on Monday at the age of 82.
An image of the then Fr Daly waving a blood-stained white handkerchief in Derry in 1972 became an enduring image of the Troubles.
Rev David Latimer said he could only speculate as to why Ms McClintock was not present at his funeral.
"I would think that every effort should have been made for the first citizen to be there," he said.
"Given the stature of Bishop Daly in this city and the work that he engaged in, not only as bishop but in the incredible contribution he made as chaplain at the Foyle Hospice, I honestly think every effort should have been made.
"The person that needs to be asked is the first citizen herself.
"I would be disappointed if she was attending something and didn't allow someone to deputise for her," he said.
A spokesperson for the council said she was unable to attend the funeral and the deputy mayor was there in her absence.
The spokesperson added that a number of senior staff including the Chief Executive, John Kelpie, were also there to represent the council.
The DUP MP Gregory Campbell also defended Ms McClintock.
He was asked by the BBC if he believed her decision not to attend Dr Daly's funeral was because of the bishop's now famous role on Bloody Sunday.
"No I don't think that is the case at all," he told BBC Radio Foyle.
"If that had have been the case the DUP mayor wouldn't have... opened up a book of condolences, I wouldn't have issued a statement and the local MLA Gary Middleton also issued a statement  - so I don't think that is the case."
League One side Chesterfield have parted company with boss Dean Saunders after just six months in charge.
[NEXT_CONCEPT]
A Presbyterian minister has said the DUP mayor of Derry should have made "every effort" to attend the funeral of the former Bishop of Derry Edward Daly.