The announcement follows a report Sunday in the New York Post that Weiner had recently sent photos and sexual texts to another woman. The newspaper reported that Weiner sent one picture of his crotch last year while his toddler son, Jordan Zane, was curled in the bed next to him.
Weiner told the New York Post that he and the woman “have been friends for some time.”
“She has asked me not to comment except to say that our conversations were private, often included pictures of her nieces and nephews and my son and were always appropriate,” he said.
Weiner deleted his Twitter account Monday morning. The statement from Abedin followed.
GOP nominee Donald Trump has repeatedly alleged without evidence that Abedin was sharing classified secrets with her husband, whom he called a "pervert" and a "sleaze." He said in a statement Monday that Abedin was "making a very wise decision" by separating.
"I know Anthony Weiner well, and she will be far better off without him," said Trump, who has been divorced twice. "I only worry for the country in that Hillary Clinton was careless and negligent in allowing Weiner to have such close proximity to highly classified information. Who knows what he learned and who he told? It's just another example of Hillary Clinton's bad judgment. It is possible that our country and its security have been greatly compromised by this."
Abedin stood by Weiner through the initial 2011 revelations about his online relationships with women. Abedin was pregnant when Weiner's "sexting" habit led to his resignation from Congress in June 2011. Their son was born in December that year, and Weiner has been a stay-at-home dad for much of the time since.
A second sexting episode in 2013 helped seal defeat for Weiner as he attempted a political comeback by contesting in the New York mayor's race. A documentary about that race released this year, "Weiner," includes painful scenes with Abedin after Weiner was shown to have continued online relationships with women after he left Congress.
Abedin, 40, is the vice chair of Clinton's presidential campaign. She has worked for Clinton since she was first lady. She was the subject of a Vogue interview this month in which she talked about the pressures of parenthood during a busy political campaign.
“Many working moms feel this way — there is a lot of guilt," Abedin said. "I don’t think I could do it if I didn’t have the support system I have, if Anthony wasn’t willing to be, essentially, a full-time dad. I have in-laws who are really supportive. And I’m lucky enough to have a nanny, which I realize is completely a luxury — a lot of people aren’t able to do that. That allows me to travel and do my job."