The president-elect has said Mrs Trump and Barron will move to Washington "very soon, after he's finished with school", but has not put an actual date on the move.
But transition spokesman Jason Miller's insistence that the Trumps were "energised and excited about their new role serving the country" and it was simply concern about changing schools in the middle of the year did little to quell criticisms on social media.
"First Family resides in White House as a symbol of our country to us and and the world," wrote one Twitter user, Pamela Benbow. "Melania Trump's decision is appalling."
Others joked it was Mrs Trump's taste in interiors which had prompted the decision, while some began speculating about what the move said about the Trumps' marriage.
However, the strength of feeling is somewhat unsurprising. There are only two other First Ladies in the history of the United States who have not made the White House their home during their husbands' years as commander-in-chief: Martha Washington, because it had yet to be built, and Anna Harrison, because her husband died before she could take up residence.
But Mrs Trump's decision has its supporters.
"Good, this is what most responsible parents do with a child Barron's age," one Twitter user noted.
However, it is not out of character for Mrs Trump, who has repeatedly stressed that Barron, 10, is her focus - staying at home during the campaign to care for him in Trump Towers.
But they are far from the only mother and child to move into the White House. So how have families coped before?
William Seale, a White House Historical Association historian and author of The President's House, said President Grover Cleveland's wife, Frances Folsom Cleveland, only lived in the White House during social season.
The president bought a house during his first term, where Mrs Cleveland spent most of her time. The first lady referred to the first home as "Oak View" but it was more commonly known as "Red Top" because of its red roof.
But the young bride, who was age 21 when she married the 49-year-old president, was the only first lady to be married in the White House.
"The concern of children staying back to finish school - that's more typical than not," Mr Seale said.
"It seems not very unusual to me that she would want the child to finish this year of school. I don't find it very surprising."
Mr Seale noted that the children of President John Tyler, who became president after William Henry Harrison's death, were not immediately moved to the White House.
James Madison's wife, Dolley Madison, also sent her son from her first marriage, Payne Todd, away to school.
There have been two sets of school age children living in the White House in the past three decades: Chelsea Clinton, who was 12 at the time, and Malia and Sasha Obama, who were 10 and seven respectively.
They also had to move across the country when their fathers became president - but all three lived at 1600 Pennsylvania Avenue from the day of the inauguration.
In fact, the Obamas avoided the problem of the girls having to change school mid-term by moving to Washington early, allowing them to start a new school a few weeks before Dad was inaugurated in January 2009.
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Mrs Trump has indicated Barron will be her top priority, with everything else coming second. Reading between the lines, it suggests she will not be taking on the full-time role predecessors like Mrs Obama have.
Officially, the role of the first lady is only ceremonial - she is supposed to be the White House's hostess, organising and attending functions with or without their spouses.
In more recent times, they have also sought out causes to support and promote. Mrs Obama has used her time backing a number of initiatives and projects, including Let Girls Learn, that aims to help girls around the world go to school and stay in school.
The first lady occupies a very public role, according to Mr Seale.
"It gives a kind of personal side to the White House. It might even be considered vital to the public's perception of the president," he said. "[The president] is an administrator and a he is a symbol and I think the first lady's role is very important to that symbol part."
Lou Henry Hoover, wife to President Herbert Hoover, was the first president's wife to really take on an active public role, Mr Seale said.
Her immediate successor, Eleanor Roosevelt, also served as a more visible first lady in her husband's administration.
One notable first lady who was reluctant to step into the public role was Nancy Reagan, according to Mr Seale.
Mrs Reagan, who had a big influence on her husband's presidency and would later become known for her anti-drug campaign, was at first only focused on being a supportive wife.
"Her big interest in the world was her husband," Mr Seale said, adding that she was a very private person.
As to what Melania's priorities will be there is only one hint - she is interested in tackling cyber-bullying.
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It has happened in the past. However, not when the president's wife has still been alive.
Thomas Jefferson's daughter Martha Jefferson Randolph took the role in 1801, while Angelica van Buren took up the duties of a first lady after marrying President Martin van Buren's son in 1838. Both men had lost their wives almost 20 years earlier.
However, could Ivanka Trump - described as her father's "proxy wife" by Vanity Fair during the election campaign - take up some of the responsibility from her step-mother?
There is more recent precedent, too. Chelsea performed some of her mother's duties during the final days of her father's presidency, while Mrs Clinton concentrated on her own political career.
The White House can be whatever the family makes it.
Chelsea was known to do her homework in the Oval Office from time to time, while she also hosted sleepovers for friends - which could mean they found themselves sitting with the President the next morning, as Bill Clinton always tried to have breakfast with his daughter.
Both Hillary Clinton and Michelle Obama fit their duties as First Lady around their children, and both families asked for the press to respect their daughters' privacy - requests which were, on the whole, respected.
The Obamas are also strict about putting time aside for the girls: family dinner takes place every night at 18:30. Mr Obama has said only a national emergency will stop him joining his family.
"The surprising truth is that being in the White House has made our family life more 'normal' than it's ever been," the President said in an interview with US magazine More earlier this year.
It is a response echoed by Chelsea about her own years.
She told the Huffington Post: "I was always deeply aware that I was living in history. But then I would have dinner with my parents at the kitchen table every night. There was so much about my life that also was normal."
The revelation that Melania and Barron Trump would not be joining Donald in the White House in January has raised eyebrows in some quarters, and garnered praise in others.