"Larry is currently in good condition at Walter Reed National Military Medical Center and his doctors expect he will make a full and speedy recovery," Ms Sanders said.
Mr Kudlow's wife, Judith, told the Washington Post that her husband was "doing fine."
Mr Kudlow joined the Trump administration earlier this year and has taken a tough stance on trade.
The US imposed tariffs on steel and aluminum imports from the EU, Canada and Mexico on 1 June, setting the scene for a tense G7 meeting hosted by Canadian Prime Minister Justin Trudeau over the weekend.
The summit ended with Mr Trudeau vowing to press ahead with retaliatory tariffs and Mr Trump retracting his endorsement of the joint statement and lashing out at his host.
Mr Kudlow has defended the new tariffs and said his boss should not be blamed for trade tensions.
After the summit, Mr Kudlow told CNN that the president and his team had gone to the summit "in good faith" but that Mr Trudeau had "stabbed us in the back."