Cohen is asking to delay proceedings in Los Angeles for 90 days, arguing that any statement could affect a criminal investigation into his business dealings in New York.
That investigation saw the FBI raid his offices for information -- including on a nondisclosure agreement Daniels signed days before the 2016 presidential election.
Invoking the fifth will allow Cohen to avoid revealing sensitive information in the wider probe into him.
"Based upon the advice of counsel, I assert my 5th amendments rights in connection with all proceedings in this case due to the ongoing criminal investigation by the FBI and U.S. Attorney for the Southern District of New York," Cohen declared in a court document filed by his lawyer.
Cohen has admitted to paying Daniels $130,000 from his own pocket shortly before the 2016 election as part of the agreement to silence her. Trump has denied knowledge of the payment.
"Never before in our nation's history has the attorney for the sitting President invoked the 5th Amend in connection with issues surrounding the President," Daniels' lawyer, Michael Avenatti, wrote on Twitter.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.