White House Press Secretary Stephanie Grisham also expressed distaste for the quip.
"Classless move by a Democratic 'witness'. Prof Karlan uses a teenage boy who has nothing to do with this joke of a hearing (and deserves privacy) as a punchline," Grisham tweeted. "And what's worse, it's met by laughter in the hearing room. What is being done to this country is no laughing matter."
Karlan, hours later, apologised for the remark, but not without making another dig at the president.
"I want to apologise for what I said earlier about the president's son. It was wrong of me to do that," Karlan said during the hearing. "I wish the president would apologise for the things that he's done that's wrong, but I do regret having said that."
Karlan was one of three legal scholars asked to testify by the Democrats in the first Judiciary Committee impeachment-inquiry hearing. The sole GOP witness was Jonathan Turley, a professor at George Washington University Law School.