The Hollywood legend was appearing with director David O Russell and co-star Bradley Cooper on Katie Couric's chatshow when he became emotional.
O Russell had been discussing his son, who has a mood disorder similar to Bradley Cooper's character on Katie.
Couric asked De Niro if the director's personal story had given him a greater responsibility than some of his previous films.
"Oh, of course," he said, before he was visibly moved by the subject matter.
"I don't like to get emotional," he added. "But I know exactly what he's going through."
David O Russell said: "When I first was in his apartment and I was talking to him about the screenplay, this is what happened.
"I thought he was having hay fever and I realised he was having an emotional reaction. I sat there and I watched Robert De Niro cry for 10 minutes."
Silver Linings Playbook is nominated for three BAFTAs and eight Academy Awards.
Robert De Niro said last year that he has no plans to retire from acting in the near future.
Watch the trailer for Silver Linings Playbook below: