The Oscar-nominated actor, who is reprising his role as billionaire playboy Tony Stark, injured his ankle while performing a stunt.
Marvel Studios issued a statement saying there would be “a short delay in the production while he recuperates”.
Iron Man 3, co-starring Guy Pearce and Sir Ben Kingsley, is scheduled to be released in 2013.
The third film reunites Downey Jr with regular co-stars Gwyneth Paltrow, Jon Favreau and Don Cheadle.
Downey Jr first debuted in the blockbuster role in 2008, to huge public and critical acclaim – with the film making $585m (£372m) at the worldwide box office.
He returned to the role in an equally successful sequel in 2010, with the global box office peaking at $623m (£396m).
Read more: BBC