Murray plans to enter a treatment program for alcohol abuse, the team and Murray said in a statement Wednesday.
The 66-year-old Murray has been with the organization since 2005 and has run the hockey operations since November 2008, the third-longest active tenure for a GM in the NHL.
"I want to apologize to anyone adversely affected by my behavior," Murray said. "I vow to make changes to my life, starting with enrolling in a treatment program. ... As I step away from the Ducks, I will focus my attention on where it should be: improving my life for the betterment of my family and friends."
Jeff Solomon, who joined the Ducks' front office in May, will be Anaheim's general manager while the club seeks a permanent replacement, owners Henry and Susan Samueli said in a statement. The search could last until the offseason next year.
The Samuelis said they "apologize on behalf of the organization to anyone affected by misconduct from Bob. We expect every member of our organization to be treated with respect and will not stand for abuse of any kind. ... While we do not condone his conduct, we fully support his efforts to improve his physical and mental health by asking for help."