The club has brought in the external law firm Sheppard Mulling to conduct an independent investigation after information emerged that Murray had behaved inappropriately and that the club had conducted an internal investigation into the matter.
Anaheim does not want to go into details about the accusations.
Assistant general manager Jeff Solomon joins as acting during the investigation.
It is the second club top that has undergone an internal investigation this year.
Chicago's Stan Bowman chose to resign after an internal investigation into how the club in 2010 handled allegations of sexual abuse directed against the former video coach Brad Aldrich.