The BBC said Iksanov was removed from his post following a series of scandals.
Iksanov is accused of mismanaging the Bolshoi's $1 billion renovation, which ran years over schedule and budget, and of harassing principal dancer Nikolai Tsiskaridze, whom he accused of being involved in an acid attack that left the ballet company's artistic director Sergei Filin mostly blind.
Tsiskaridze has vehemently denied any involvement in the assault for which three other people are awaiting trial.
"A difficult situation had developed around the theater and the troupe -- everything pointed to the need for renewal," the British broadcaster quoted Culture Minister Vladimir Medinsky as saying about the decision to replace Iksanov.
Iksanov had been the head of the Bolshoi Theatre for the last 13 years and had more than a year left on his contract.
Medinsky said Iksanov will have a role advising Urin, former general director of the Stanislavsky Musical Theatre, until Iksanov's contract runs out, the BBC said.