The photo, which Mr Trump posted in a since-deleted Tweet, showed Maxwell at the 2010 wedding of Chelsea Clinton, Bill and Hillary's daughter. Mr Trump added the caption: "Birds of a feather..."
But the move soon prompted a backlash, with fellow Twitter users digging up an array of photos that appeared to show Maxwell with his father, Donald Trump.
MSNBC producer Kyle Griffin, replying to Eric's tweet, said: "Does the president's son not know that there are photos of Donald Trump with Maxwell?
Another Twitter user shared a photo of the president and Ms Maxwell and said: "Eric may be on to something."
A third said: "It's like it's eric's [sic] first day on earth."
Maxwell was arrested on Thursday by the FBI and charged with enticing a minor to travel to engage in criminal sexual activity, transporting a minor with the intent to engage in criminal sexual activity, conspiracy and perjury.
Does the president's son not know that there are photos of Donald Trump with Maxwell?— Kyle Griffin (@kylegriffin1)July 2, 2020
All of these charges are in connection with offences committed by Jeffrey Epstein, who died last year.
Acting U.S. Attorney of the Southern District of New York Audrey Strauss said: “As alleged, Ghislaine Maxwell facilitated, aided, and participated in acts of sexual abuse of minors. Maxwell enticed minor girls, got them to trust her, and then delivered them into the trap that she and Jeffrey Epstein had set.
"She pretended to be a woman they could trust. All the while, she was setting them up to be abused sexually by Epstein and, in some cases, Maxwell herself. Today, after many years, Ghislaine Maxwell finally stands charged for her role in these crimes."
The Clintons gave a statement to Politico in 2015 attempting to distance themselves from Epstein and Maxwell.
Their chief of staff said: “It wasn’t until 2015 that Chelsea and [her husband] Marc became aware of the horrific allegations against Ghislaine Maxwell and hope that all the victims find justice.
“Chelsea and Marc were friendly with her because of her relationship with a dear friend of theirs. When that relationship ended, Chelsea and Marc’s friendship with her ended as well.”