Author Kate Andersen Brower told CNN that the decision to not unveil the portrait charts a dark new course in US politics.
"Presidential portrait unveilings are one of the three events that bring former presidents together. This level of animosity between a sitting president and his predecessors is unprecedented in modern history," she said.
'Obamagate'
The startling development comes as Trump continues to push a narrative that Obama is involved in a "deep state" conspiracy that he has dubbed "Obamagate".
Trump has stated, without evidence, that he believes Obama had committed unspecified crimes, and some of his supporters have encouraged criminal inquiries into Obama and his vice-president Joe Biden for what they say are abuses during the investigation into ties between Russia and Trump's 2016 presidential campaign.
Trump has used his favourite medium to sell the theory, repeatedly tweeting what he has called "the biggest political crime and scandal in the history of the USA".
But Obama had a simple one-word response to the barrage of tweets.
Trump's efforts may not amount to any real-world consequences as Attorney General William Barr has signalled that he would not be swayed by political pressure to investigate the president's opponents.
- Additional reporting, AP