The 50-year old, who reprises his role as Tony Stark/Iron Man in superhero film "The Avengers: Age of Ultron", appeared to be puzzled by British television journalist Krishnan Guru-Murthy's questions as they turned personal.
"Are we promoting a movie?" Downey Jr asked after the news presenter referred to comments he had made after serving a prison sentence.
The interview, part of a promotional round in which journalists are allocated five-minute slots with the cast, began smoothly with Downey Jr talking about his role and "The Avengers" sequel, which had its European premiere in London this week.
But the tone shifted as the journalist asked about the actor's "dark periods ... taking drugs and drinking" and whether he was "free of all that".
"I'm sorry, I really don't ... What are we doing?" the actor said before walking out.
The interview aired on Britain's Channel 4 News on Wednesday night and Guru-Murthy, who posted it on his Twitter feed, faced angry comments from viewers criticizing his line of questioning.
Guru-Murthy upset film director Quentin Tarantino in 2013 by asking him a question about screen violence.