"I don't think he gave anything away," Kudlow said on "Squawk on the Street." "I think this is all according to routine, law and custom."
About an hour before the report was released, Trump tweeted, "Looking forward to seeing the employment numbers at 8:30 this morning."
The monthly report is embargoed, and it's kept under tight wraps because it frequently moves the financial markets.
Kudlow, director of Trump's National Economic Council, spoke shortly after the Bureau of Labor Statistics reported the U.S. economy continued to add jobs in May, with nonfarm payrolls up 223,000. That was higher than the growth of 188,000 positions that economists had expected.
The unemployment rate fell to an 18-year low 3.8 percent last month. Estimates had called for a steady jobless rate of 3.9 percent.
White House Press secretary Sarah Huckabee Sanders said Trump's tweet was appropriate because "he didn't put the numbers out."
Kudlow said he did indeed give Trump the numbers on Thursday afternoon, saying it's his call on whether to give the president the report ahead of time.
"I tracked him down on Air Force One. I wanted him to know the numbers," Kudlow said.
On the report itself, Kudlow said the job gains reflect that the U.S. has "entered into the longest prosperity in a couple of decades."