In a statement issued by JLM on Friday evening, Mr Caplin said he had the "highest regard" for Dr Lipstadt.
He added: "I was trying to make the point (albeit clumsily) make the point about the importance of tackling antisemitism within the Labour Party.
"I have the highest regard for Professor Deborah Lipstadt and for the incredible work she has done over the years in challenging Holocaust denial and I apologise unreservedly to her."
He continued: "When someone of Professor Lipstadt's expertise and prominence speaks about the nature of antisemitism in the Labour Party, we should all listen and act."
Mr Caplin, a former defence minister in Tony Blair’s government, was confirmed as JLM chair in June.
A former Labour MP for Hove, in Sussex until 2005, Mr Caplin replaced former chair Jeremy Newmark after he resigned earlier this year.