Frieden, who also is a former New York City health commissioner, was arrested earlier Friday on three charges: forcible touching, sex abuse and harassment. Though they knew each other, they were not believed to have an intimate relationship.
It was reported to police in July.
Frieden is expected to be arraigned on Friday afternoon.
Frieden remained in custody on Friday, Muniz said.
An order of protection was issued, and Frieden is to have no contact with the alleged victim, according to the district attorney's office.More news: Minister Dan Tehan dodges dumping of Malcolm Turnbull question
More news: Rep. Duncan Hunter says he's eager for trial
More news: Jennifer Garner took Ben Affleck back to rehab
In the 1990s, he led a tuberculosis control program in NY that lowered the incidence of cases that were resident to multiple drug treatments.
The judge ordered Frieden to refrain from any contact with the woman and to surrender his USA passport.
Frieden is now president and CEO of the global health non-profit Resolve to Save Lives. "In all of my experiences with him, there have never been any concerns or reports of inappropriate conduct".
The president of Vital Strategies, Jose L. Castro, came out in support of Frieden. "This assessment determined there have been no incidents of workplace harassment", he said. That led to work with the World Health Organization's TB program in India.
He was behind some of the biggest public health initiatives in city history, including prohibiting smoking in bars and outlawing trans fats in restaurants.
Dr. Thomas "Tom" Frieden, former director of the Centers for Disease Control and Prevention (CDC), in a 2016 photo.