Nabokov straddles the line between Modernism and Postmodernism. He was born at the turn of century (along with other modernists such as Hemingway or Crane), but lived well past the middle twentieth century, which is when Postmodernism really begins. Postmodernism is a very complex phenomenon/movement, but one of its key characteristics is metafictionality.
This is an even further extension of modernist self-reflexivity. The term "metafiction" refers to a fiction that is about fiction and in which fictions proliferate (fiction upon fiction upon fiction). For example, a character might be aware that she is inside a novel and rebel against her author. Or, an author might make an appearance within a novel and have a conversation with a character. Or, a character might escape from one novel into another, or might write a novel that contains another novel.