Spokeswoman Risa Heller said Weiner has left for professional treatment and will focus on "becoming a better husband and healthier person."
Heller also said the New York Democrat wants the leave of absence so he can be evaluated and work out a course of treatment.
The statement doesn't say what Weiner would be treated for.
Mere hours before the statement was released, leading Democrats demanded Weiner's resignation after he admitted to online contact with a teenager.
National party chairman Debbie Wasserman Schultz said Saturday that Weiner's behavior is "indefensible" and his role in Congress is "untenable."
The Florida congresswoman said, "this sordid affair has become an unacceptable distraction" for everyone.
House Minority Leader Nancy Pelosi has said Weiner "needs help" and he should get some "without the pressures of being a member of Congress." She said the decision of his resignation should be up to him and his constituents
In a recent poll of registered voters in Weiner's district, 56 percent said he should stay in office while 33 percent said he should leave.
The 46-year-old congressman admitted Friday that he had been communicating with a 17-year-old girl from Delaware.
Weiner's office said those communications were neither explicit nor indecent. The New York Times reported Weiner said he exchanged at least five private messages on Twitter with the girl.
New Castle County police said they've interviewed the girl, and she disclosed no information regarding any criminal activity.
It's the latest turn in a scandal that has some members of Congress saying the 46-year-old congressman should step down, after he admitted to sending sexually explicit messages to women online.
Meantime, Weiner is speaking out about how his pregnant wife, Huma Abedin, is handling the sexting scandal. When a reporter asked how she was holding up, Weiner responded by saying she's doing well and added that "she is a remarkable woman who is working very hard."
Abedin is a top aide to Secretary of State Hillary Rodham Clinton. Friends have said she's more saddened than angry over her husband's behavior.
Weiner does have supporters though, including Rep. Charles Rangel, D-N.Y.
"He wasn't going with prostitutes. He wasn't going out with little boys," Rangel said. "I know immoral sex when I hear it from other members, and no one has screamed for their resignation so I don't know why they're selecting Anthony," he added.
Rep. Xavier Becerra, D-Calif., appearing on Eyewitness Newsmakers has a different view than Rangle.
"I believe he should be investigated, and we'll find out. If he violated the law, or one of our rules of our ethics, then he'll know what to do, he's got to go. But right now, I think we're trying to find out what the ethics committee will tell us," said the Los Angeles lawmaker.
At least nine House members and three senators said Weiner should resign. Weiner has repeatedly said he would not.