Albrecht, who said Tuesday he was taking a leave of absence to regain control of his alcoholism, said a day later that he was resigning as chairman and CEO "at the request of Time Warner."
His resignation also came after the Los Angeles Times reported on Wednesday that HBO in 1991 paid a settlement of at least $400,000 to a subordinate and former lover of Albrecht's after she accused him of shoving and choking her.
"This is the right decision for the company," said Time Warner chairman and CEO Richard Parsons. "We thank Chris for all his contributions to Home Box Office over the years."
Albrecht had been chief of programming at HBO since 1995 and became CEO in 2002. He presided over the company's greatest successes with "The Sopranos" and "Sex and the City," but the company was having trouble developing its next generation of hits.
Bill Nelson, HBO's chief operating officer, will run the company until a permanent chairman is selected, Time Warner said.
Albrecht was arrested outside the MGM Grand's valet parking lot shortly after 3 a.m. on Sunday, after officers reported seeing him fight with a woman identified as his girlfriend. On Tuesday, Albrecht said he had a drinking problem and, though he had been sober for 13 years, had recently slipped back into drinking.
Of his resignation on Wednesday, Albrecht said that he did it "for the benefit of my Home Box Office colleagues, recognizing that I cannot allow my personal circumstances to distract them from the business."
The Los Angeles Times story about the 1991 incident said Albrecht had been involved with a woman who worked for him at the time at HBO Independent Productions. The company reportedly paid the settlement following an encounter that occurred after the woman told Albrecht she was dating someone else.