The Godfather (unlike The Godfather Part II) doesn't use any flashbacks and it doesn't delve into a bunch of seemingly unrelated subplots that converge to some degree. But it does have a kind of narrative break.

When Michael heads off to Sicily, his story diverges from the main narrative. He lives a separate and radically distinct life, much different from what he'd had back in New York and with Kay Adams. But when a bomb blows his Sicilian wife to smithereens, he realizes that he's been called back to New York and his former life. Then, his story rejoins the main narrative.

The early sequence with the movie producer and the horse's head is a bit of a disjunction too. It's kind of like a short story nestled within the greater story, or a prologue to the rest of the movie. It's not entirely unrelated to the rest of the action, since it demonstrates what Don Corleone is willing to do to help his kin out, but it's also different enough to be worth mentioning.