Trump penned news of his chief economic aide's health while in a convoy traveling to meet Kim Jong Un.
The White House didn't immediately comment on his condition.
Kudlow's wife, Judith Kudlow, told The Washington Post in a brief conversation on Monday evening that Kudlow was doing well and recovering. The president tweeted that Kudlow is now at Walter Reed Medical Center.
Kudlow joined the president at the Group of Seven summit in Quebec on Friday and Saturday.
Mr. Trump hired him in April to replace Gary Cohn as the head of the National Economic Council, reportedly because he enjoyed Mr. Kudlow's combative television appearances. In return, Trump called the Canadian leader "very dishonest" and "weak", and said the United States would not endorse a joint G7 communique.
"In an interview with CNN on Sunday, Kudlow said: "(Trudeau) really kind of stabbed us in the back".
Kudlow has been at the center of the US President's trade feuds in recent months, joining US delegations in Beijing and Canada to address trade disputes.
There was no additional information from the White House or second source, rather it was only Trump's twitter account.
He is better known as a TV pundit, known for his bullish pro-trade ways and comical manner as a 25-year-veteran of business network CNBC.
Senior White House economic adviser Larry Kudlow speaks during a briefing at the White House in Washington.