In an article on the official website of the White House titled, "My personal experience with COVID-19", Mrs Trump also disclosed that she had also tested negative.
She also told that her son Mr Barron is a "strong teenager" who displayed no indications. He later called Barron "beautiful" and "free" at a campaign rally in Iowa on Wednesday evening.
In an open letter from the White House, the First Lady said the virus "hit me all at once and it seemed to be a roller coaster of symptoms in the days after".
Melania meanwhile admitted that she only experienced mild symptoms; body aches, a cough, headaches and fatigue. She thanked well-wishers and said the support from White House physicians and other medical staff inspired her to be "even more grateful and in awe of caretakers and first responders everywhere".
The President has shown little concern about spreading the virus, however, traveling in recent days to speak before crowds of thousands, and has baselessly claimed he is now "immune" to the virus.
Last month, both the President and the First Lady were diagnosed with Covid-19.
The first lady further said that it gave her the opportunity to reflect on her family and on the million of Americans affected by the virus.
When asked about his son on Wednesday, President Donald Trump said he was "fine".
The US Department of Justice claims the author of "Melania and Me: The Rise and Fall of My Friendship with the First Lady" breached her non-disclosure agreement (NDA) and that she failed to submit a draft copy of the book for government review.
However, Melania was not hospitalized, unlike the president. His positive result came in a subsequent test, the first lady wrote. His illness and especially his three-day hospital stay were followed with as much attention as his return to the public. This allowed them to take care of each other and spend time together as well since they are quarantining together.
An event at the White House on 26 September, for the unveiling of Mr Trump's Supreme Court nominee Amy Coney Barrett, is thought to be the root of the localised outbreak.
Trump and the NBC host will be socially distanced at the outdoor venue and the audience will wear masks, NBC added.