Trump had mocked Republican rival Carly Fiorina in an interview with Rolling Stone published Wednesday.
"Look at that face!" Trump said, about Fiorina. "Would anyone vote for that? Can you imagine that, the face of our next President?!"
Trump and Jindal also exchanged words on social media Thursday, a day after Jindal suggested Charlie Sheen should be Trump's running mate.
"I think it’s pretty outrageous for him to be attacking anybody’s appearance when he looks like he’s got a squirrel sitting on his head," Jindal told CBS Thursday. "I think he should stop attacking other people's appearances."
Watch Jindal's comment: