Murray, 35, one of the Football League's youngest managers, had been in charge for just short of two years.
"It is with regret that Mansfield Town Football club announces that Adam Murray has decided to leave his position as manager," read a statement on the club's official website.
The club's announcement was made after talks between Murray and club chairman John Radford following Saturday's 4-0 Sky Bet League Two defeat at Portsmouth.
The statement added: "Following a meeting between Adam and chairman John Radford, Adam asked to vacate his position as manager in the best interests of both himself and Mansfield Town Football Club.
"The club can also confirm that first team coaches Karl Hawley and Richard Cooper have left the club.
"Under-21s head coach Mike Whitlow and youth-team manager John Dempster will take temporary charge of first-team affairs as a search for a permanent replacement takes place.
"The club will be making no further comment at this stage."
Murray, who had three different spells with the Stags as a player, became the youngest Football League manager when he was named permanent boss in December 2014.
Murray said: "I have been with the club for over 14 years and having discussed it with my management team we have decided that it is time for a change.
"We are immensely proud of what we have achieved, moving both the club forward and achieving its highest league position in over 10 years."
Radford paid a glowing tribute to Murray, who combined the roles of captain and assistant manager when the club won promotion back to the Football League in 2013.
"I've worked with Adam for a long time and respect him immensely," Radford said.
"The decision by Adam to part ways was made with a very heavy heart.
"Adam will always be in Mansfield Town's hall of fame
He has served the club magnificently as both a player and for almost two years, a manager, and I sincerely wish him well for the future."
Source : PA