The social media giant banned Mr Trump from its platform in January following riots by his supporters on the Capitol building in Washington.
Lara Trump, a new Fox News contributor, posted a video of herself interviewing Mr Trump on a range of issues.
She later posted a screenshot of an email she received from Facebook warning her of the ban.
"In line with the block we placed on Donald Trump's Facebook and Instagram accounts, further content posted in the voice of Donald Trump will be removed and result in additional limitations on the account," an email from "Katelyn" read.
Lara Trump, who is married to Mr Trump's son Eric, instead posted the interview for her own online show The Right View on the video platform Rumble and linked to it from her Facebook page.
"And just like that, we are one step closer to Orwell's 1984. Wow," she commented on her Instagram account.
Long-time Trump supporter and Fox News TV host Sean Hannity described the move as "extreme censorship" in a tweet.
Facebook's suspension of Mr Trump's account on 7 January - a day after the Capitol riots - is being reviewed by its new Oversight Board, which was set up to rule on controversial moderation decisions.
Defending the ban at the time, Facebook chief Mark Zuckerburg said: "We believe the risks of allowing the president to continue to use our service during this period are simply too great."
Donald Trump was also banned from Twitter and YouTube.