"After long and painful consideration and work on my marriage, I have made the decision to separate from my husband", she said in the statement.
She adds: "Anthony and I remain devoted to doing what is best for our son, who is the light of our life".
Abedin first worked for Clinton in the 1990s as an intern when Clinton was first lady.
A friend of Abedin, who spoke on condition of anonymity because of the sensitivity of the breakup, said she was with her young son, Jordan, and her family members in the Hamptons during the weekend.
Former New York congressman Anthony Weiner attends the start of the second day of the Democratic National Convention at the Wells Fargo Center on July 26.
But as NBC News reported on Monday, the Republican nominee, who is now using Weiner's marital troubles because he thinks it will benefit his candidacy, has donated thousands of dollars to the Democrat's past political campaigns dating back to 1997.
"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", he continued.
Last month, Trump referred to Weiner to argue that Clinton is a security risk, labeling Weiner "a sleazeball and pervert".
He recently refused to answer when asked whether he was still sexting, telling The New York Times Magazine in an interview published August 16: "I'm not going to go down the path of talking about any of that".
Weiner served in the US Congress, representing his district in New York City from 1999 to 2011.
Reacting to the latest scandal on Monday, Mr Trump said in a statement: 'Huma is making a very wise decision. "Who knows what he learned and who he told?"
Abedin and Weiner were married in 2010 at a wedding officiated by former President Bill Clinton.
In an interview with Vogue, according to the New York Times, Abedin talked about how much she has relied on Weiner during the campaign.
The disgraced former U.S. congressman, Anthony Weiner, and his wife, Huma Abedin, are to separate.
The New York Post published photos late Sunday that it said Weiner had sent past year to a woman identified only as a "40-something divorcee" who lives in the West and supports Republican Donald Trump.
Leathers also commented on Weiner's mental health.
The announcement of the separation came after the Post showed that Mr Weiner had exchanged photos with the woman. After polls put him in contention to replace Michael Bloomberg he became embroiled in yet more controversy with sexually charged messages once again the focus. Not that it's any of anyone's business, but based on Abedin's track record of loyalty to Clinton, it's not surprising she would remain fiercely loyal to her husband as long as she possibly could.