The convicted sex-offender is accused of paying underage girls for massages and molesting them at his homes in Florida and New York, law enforcement officials who spoke on condition of anonymity told The Associated Press.
The allegations date back to the early 2000s.
Detained on Saturday in New York and is expected to appear on Monday in federal court, one of the officials said.
Epstein is being held at the Metropolitan Correctional Center in Manhattan, according to the Federal Bureau of Prisons website.
The 66-year-old's arrest, first reported by The Daily Beast website comes amid renewed scrutiny of a once-secret plea deal that ended a federal investigation against him.
That deal, which is being challenged in Florida federal court, allowed Epstein to plead guilty to lesser state charges of soliciting and procuring a person under age 18 for prostitution.
Averting a possible life sentence, Epstein was instead was sentenced to 13 months in jail. The deal also required he reach financial settlements with dozens of his once-teenage victims and register as a sex offender.
Epstein's deal was overseen by former Miami US attorney Alexander Acosta, who is now Mr Trump's labour secretary.
Mr Acosta has defended the plea deal as appropriate under the circumstances, though the White House said in February that it was "looking into" his handling of the deal.
US district Judge Kenneth Marra of Florida ruled earlier this year Epstein's victims should have been consulted under federal law about the deal, and he is now weighing whether to invalidate the non-prosecution agreement, or NPA, that protected Epstein from federal charges.
It was not immediately clear whether the cases involved the same victims since nearly all have remained anonymous.
Federal prosecutors recently filed court papers in Florida case contending Epstein's deal must stand.
"The past cannot be undone; the government committed itself to the NPA, and the parties have not disputed that Epstein complied with its provisions," prosecutors wrote in the filing.
They acknowledged, however, that the failure to consult victims "fell short of the government's dedication to serve victims to the best of its ability" and that prosecutors "should have communicated with the victims in a straightforward and transparent way".
The victims in the Florida case have until Monday to respond to the Justice Department's filing.
According to court records in Florida, authorities say at least 40 underage girls were brought into Epstein's Palm Beach mansion for what turned into sexual encounters after female fixers looked for suitable girls locally and in Eastern Europe and other parts of the world.
Some girls were also allegedly brought to Epstein's homes in New York City, New Mexico and a private Caribbean island, according to court documents.
In an interview with New York Magazine in 2002, Mr Trump said he had known "terrific guy" Jeffrey Epstein for 15 years.
“He’s a lot of fun to be with. It is even said that he likes beautiful women as much as I do, and many of them are on the younger side," Mr Trump said.
There are claims, previously denied by Buckingham Palace, that Prince Andrew lobbied for Epstein to be treated leniently when he was forced to serve his year in jail. The friends were also photographed walking in New York’s Central Park in February 2011.
HIs latest arrest also came just days after a federal appeals court in New York ordered the unsealing of nearly 2,000 pages of records in a since-settled defamation case involving Epstein.
US senator Ben Sasse released a statement on Saturday calling for Epstein to be held without bail pending trial.
"This monster received a pathetically soft sentence last time and his victims deserve nothing less than justice," Mr Sasse said in the statement. "Justice doesn't depend on the size of your bank account."
Mr Epstein's defence lawyer has been approached for comment.
Additional reporting by Associated Press
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