US District Judge Denise Cote denied Apple's request to delay enforcement of the order that stems from a ruling in July that Apple illegally colluded with book publishers to fix prices.
She gave Apple only until Monday to accept compliance, but said it could get an extension from an appellate court if it files a request by Saturday.
An Apple attorney, Theodore Boutrous, said an appeal would be filed.
The judge's 64-page order harshly criticized Apple for failing to work with the court-appointed monitor, former prosecutor Michael Bromwich, and said she appointed him only after Apple made it clear it would not reform its practices on its own.
(Also see: Apple hindering ebook anti-trust work, says NY monitor)
"The court created breathing room for Apple to unilaterally revise and improve its compliance program, even after Apple had failed to take the opportunities which were given to it this past summer to show that it would do so without the imposition of a monitor," Cote wrote.
"That said, the monitor has important work to do, and where that work properly includes interviews of board members or executives, then the monitor must be permitted to conduct those interviews."
The judge said Apple failed to show it would be "irreparably harmed" by complying with the court order or with the monitor.
She said that since the monitor began work three months ago, Apple has permitted only 13 hours of interviews, and that seven of the 11 people interviewed were attorneys.
"A monitorship would be of little use at all if a monitor were only permitted to receive, review and opine on company-vetted documents," the judge said.
"Apple cites to no case holding that a monitor may never conduct interviews and there are many examples to the contrary."
The Northern California-based maker of iPads, iPods, iPhones and Macintosh computers has a had a strained relationship with Bromwich since he was appointed.
The company protested Bromwich's intent to question chief executive Tim Cook, lead designer Jony Ive, board member Al Gore and other top executives who aren't involved in day-to-day operations.
Apple also objected to the $1,100 hourly rate for himself and the $1,025 rate for his legal support team.
Judge Cote said Apple must raise any objections with Bromwich himself or the Department of Justice, and if they cannot resolve the matter, by petitioning the court.
"The deterioration of the relationship between Apple and the monitor is unfortunate and disappointing," she said.
(Also see: Apple seeks removal of monitor appointed in ebooks case)
"Hopefully, that relationship can be 'reset' and placed on a productive course. But it is strongly in the public's interest for the monitor to remain in place."
The trial focused on a six-week period in late 2009 and early 2010 during which Apple negotiated contracts with publishers ahead of its iPad launch and effectively reshaped the market for electronic books with a new pricing scheme.
For the latest tech news and reviews, follow Gadgets 360 on X, Facebook, WhatsApp, Threads and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel. If you want to know everything about top influencers, follow our in-house Who'sThat360 on Instagram and YouTube.