East Wing communications director Stephanie Grisham confirmed to CNN that the first lady's decision to forgo the trip was based on "scheduling and logistical issues."
A week ago, Grisham told CNN the first lady would be attending the annual meeting of influential financial leaders and business titans in a show of support for her husband, who intends to give remarks during his visit.
The President's own trip to Davos was also in flux until several hours ago, due to the government shutdown, which has been now been resolved.
White House press secretary Sarah Sanders had said Monday that if the government reopened, Trump would keep his promise to attend.
"The President's delegation will leave tomorrow, and the President will continue on his trip later in the week," she said, in the event of the shutdown ending.
Melania Trump has not made a public statement since January 12, when news of a possible payoff from her husband's lawyer to porn star Stormy Daniels to cover up an alleged affair was first reported by The Wall Street Journal
The first lady did, however, depart with the President later that day to Mar-a-Lago for the long holiday weekend, although she was not spotted with him during two evening dinners hosted by Trump, one with former New York Mayor Rudy Giuliani and another with House Majority Leader Kevin McCarthy.
She tweeted on January 15 in honor of Martin Luther King Jr. Day, something her husband was criticized for not doing.
On Saturday, Melania Trump marked the one-year anniversary of her husband's inauguration by tweeting an image to mark the occasion that did not include the President, but rather was of herself, her arm linked with a military escort, at Trump's inaugural swearing-in ceremony.
She posted that the past year had been filled with "many wonderful moments," but she did not mention the President by name.