Associated Press/Gerald Herbert
Republican presidential candidate Donald Trump.
"Huma is making a very wise decision," Trump said. "I know Anthony Weiner well, and she will be far better off without him."
The GOP nominee added: "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."
The New York Post reported Sunday night that Weiner, a former Democratic congressman from New York, had been exchanging sexually suggestive images and messages with a woman - including one photo with his son, then 4 years old, in the picture.
Abedin announced in a Monday statement that she would separate from Weiner after "long and painful consideration and work" on the marriage.
"Anthony and I remain devoted to doing what is best for our son, who is the light of our life," she said. "During this difficult time, I ask for respect for our privacy."
Abedin has long been the right-hand woman for Clinton, the Democratic presidential nominee.