Trump's tweet came minutes before he is expected to meet with North Korean dictator Kim Jong Un to discuss a possible deal for the country to denuclearize.
It was not immediately known when Kudlow suffered the heart attack or what his condition was.
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Kudlow returned from Canada over the weekend after joining world leaders and members of Trump's White House circle for a combative Group of 7 summit.
"He is now in Walter Reed Medical Center", he added.
During President Ronald Reagan's first term, Kudlow was associate director for economics and planning in the White House's Office of Management and Budget.
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Kudlow, an unabashed supporter of free trade, joined the Trump administration earlier this year.
Trudeau, in a news conference on Saturday, reiterated his strong objections to steep tariffs on Canadian exports of steel and aluminum to the United States.
"Here's the thing. He really kind of stabbed us in the back", Kudlow said on CNN Sunday.
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As a commentator, Kudlow had strongly backed Trump's moves to cut taxes and reduce business regulations but was openly critical toward the president's tariffs moves.