"Joe Biden," Cruz reportedly said to some laughter while speaking at an event in Michigan. "You know the nice thing? You don't need a punchline."
The vice president's son Beau Biden died Saturday after battling brain cancer. He was 46.
Cruz then took to his Facebook page to apologize.
"It was a mistake to use an old joke about Joe Biden during his time of grief, and I sincerely apologize," he said, according to the post. "The loss of his son is heartbreaking and tragic, and our prayers are very much with the Vice President and his family."