The White House didn't immediately comment on his condition.
Kudlow joined Trump last week in Canada for the G-7 meeting of world leaders.
Kudlow has always been a respected business and economics commentator, getting his own CNBC show in 2011.
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Kudlow had worked as a White House budget aide in the Reagan administration, and had also been an informal advisor to the 2016 Trump campaign.
Mr. Kudlow is nominally in favour of free trade, but has backed Mr. Trump's nationalistic economic agenda, which has included steel and aluminium tariffs against Canada, Mexico and the European Union, as well as threats of further tariffs on autos.
Kudlow appeared on Jake Tapper's CNN Sunday Beltway show, State Of The Union, this past Sunday, accusing Canadian Prime Minister Justin Trudeau of undermining the U.S. and the G-7 confab with his comments.
"POTUS is not going to let a Canadian prime minister push him around", he said. "He is now in Walter Reed Medical Center", Mr. Trump wrote.