Publisher Henry Holt & Co. said it’s moving up its release of a new book about President Donald Trump’s administration to Friday, amid a backlash from the White House and surging interest in the title.

The book, “Fire and Fury: Inside the Trump White House” by Michael Wolff, was originally scheduled to go on sale Jan. 9, but Henry Holt said in a statement that it advanced the release date “due to unprecedented demand.”

The...