Donny are 17th with only six points from their first six league games and lost 1-0 at Gillingham on Saturday.
"The board are ambitious for a top-six finish and that is, and will remain, our aim," said a club statement.
"From today Rob Jones will take charge of first-team affairs on a temporary basis and the club has full confidence in Rob as we look forward to a tough game against Walsall this weekend."
Former Scotland international Dickov, 42, who played for Arsenal, Manchester City, Leicester and Blackburn during a lengthy playing career, was in his second managerial role.
He spent two-and-a-half years at Oldham and left in February 2013 before taking over at Doncaster in May 2013.
During his time in charge of Rovers, the club dropped down from the Championship to League One and he won 34 of the 113 matches the side played in all competitions.
In the opening game of this season, Dickov ordered his players to allow Bury to walk in an injury-time equaliser for a 1-1 draw.
Doncaster's Harry Forrester inadvertently scored when playing the ball back to the Bury goalkeeper, which then led to Leon Clarke dribbling from the centre circle to equalise unchallenged.
"I just felt the right thing for us to do was to go and let Bury score," said Dickov afterwards. "The one thing I wanted to do was to keep the good name of football and Doncaster Rovers intact."
Despite their poor start in League One, Doncaster did knock out Championship side Leeds United on penalties in the first round of the League Cup before going out to Ipswich Town in the second round.