Flynn, the former national security adviser, has pleaded guilty to lying to the FBI about those conversations, which concerned how the Trump team hoped Moscow would respond to sanctions, imposed by the Obama administration, over Russia's interference in the 2016 election.
In a statement, Trump said he was "disappointed" that McFarland had pulled out of consideration for the ambassadorship.
"K.T. served my Administration with distinction. Unfortunately, some Democrats chose to play politics rather than move forward with a qualified nominee for a critically important post," Trump's statement said.
McFarland did not immediately respond to a request for comment.
Democratic senators had placed a hold on McFarland's nomination, accusing her of misleading lawmakers about what she knew of Flynn's interactions with the Russian ambassador, Sergey Kislyak.
Last July, Sen. Cory Booker (D-N.J.) asked McFarland in writing whether she had spoken to Flynn about his contacts with the ambassador during the presidential transition.
"I am not aware of any of the issues or events described above," McFarland replied.
But court documents filed in connection with Flynn's guilty plea contradict that statement.
Flynn spoke to the ambassador in late December 2016 and asked McFarland what he should say with regard to U.S. sanctions, the court documents show.
A "senior transition official" at Trump's Mar-a-Lago resort in Florida told Flynn that members of Trump's team did not want Russia to escalate the situation, according to the documents, effectively asking Russia not to respond to the sanctions before Trump took office.
McFarland is the senior transition official, according to people familiar with the matter.
The president first nominated her as ambassador to Singapore in May. But the Senate returned her nomination to the White House.
McFarland's chances at confirmation seemed dim, but in January the administration resubmitted the nomination, indicating that the White House was confident that her involvement with Flynn and the Russian ambassador were not a barrier to her ultimately winning confirmation.