The President said he was "not a fan" of Meghan and wished Harry "luck", adding: "He's going to need it."
Meghan and husband Prince Harry did not express a preference for either candidate in the upcoming US presidential election but the Duke of Sussex called on Americans to "reject hate speech, misinformation and online negativity".
Meghan says in the video that every four years elections are referred to as the most important election of our lifetime.
"But this one is," she stressed, adding: "When we vote, our values are put into action and our voices are heard."
Though the couple mentioned neither candidate by name, a reporter at the White House asked the president his thoughts - saying the pair had “essentially encouraged people to vote for Joe Biden” in the Time 100 video.
President Trump replied: "I’m not a fan of hers and I would say this, and she probably has heard that, but I wish a lot of luck to Harry. He’s going to need it".
Harry and Meghan are now residents in the US, after quitting royal duties over what they said was unbearable intrusion and racist attitudes from the British media.
While Meghan, an American, will be able to vote in November's election.
Prince Harry confirmed in the video that he could not due to his lack of US citizenship - he added that he had not voted in UK elections throughout his life.
The duchess, who mocked then-Republican candidate Donald Trump during a 2016 television appearance, said in the video the November poll was the "most important election of our lifetime".
Meghan has previously suggested support for the Democrats, telling lawyer and feminist activist Gloria Steinem last month she was “so excited” to see fellow biracial woman Kamala Harris selected as Joe Biden's running mate.
Buckingham Palace has appeared to distance itself from the couple's comments.
When approached for comment, the Palace highlighted the fact that the duke is no longer a working royal, and said his remarks were made in a "personal capacity".