Bill Nelson, HBO chief operating officer, will take over Albrecht's duties "pending resolution of the police incident," the company said.
"We take these matters very seriously and will monitor this situation closely," Time Warner chairman and chief executive officer Richard D. Parsons said in a statement. HBO Inc. is a division of Time Warner.
In a statement sent to HBO staff members and released publicly Tuesday, Albrecht said he had been a "sober member" of Alcoholics Anonymous for 13 years.
"Two years ago, I decided that I could handle drinking again. Clearly, I was wrong. Given that truth, I have committed myself to sobriety. I intend to take a temporary leave of absence from HBO effective today, in order to go back to working with AA."
Albrecht said he was "deeply sorry for what occurred in Las Vegas this weekend and for any embarrassment it caused my family, the company I love, and myself."
He called the weekend a "wake-up call to me of a weakness I thought I had overcome long ago."
While he wasn't free to discuss the incident while authorities and his attorneys are "still determining the facts, it is my hope to do so in the near future," Albrecht said in his statement.
A call to the Clark County, Nev., district attorney's office regarding the arrest was not immediately returned Tuesday.
On Sunday in Las Vegas, the HBO chairman and chief executive was arrested for investigation of assaulting his girlfriend outside the MGM Grand casino. The arrest came just hours after Saturday's Oscar De La Hoya-Floyd Mayweather Jr. boxing match aired on pay-per-view by HBO.
Officers assigned to the match reported seeing Albrecht fighting with a woman identified only as his girlfriend in the MGM Grand's valet parking lot shortly after 3 a.m., a Las Vegas police spokesman said.
Albrecht was booked into the Clark County Detention Center and held for investigation of a misdemeanor battery-domestic assault. He was later released.
Albrecht joined HBO in 1985 as a senior vice president and was named CEO in 2002, according to his company biography.