The bare minimum
Simply put, narrative is the representation of an event or a series of events. “Event” is the key word here, though some people prefer the word “action.” Without an event or an action, you may have a “description,” an “exposition,” an “argument,” a “lyric,” some combination of these or something else altogether, but you won't have a narrative. “My dog has fleas” is a description of my dog, but it is not a narrative because nothing happens. “My dog was bitten by a flea” is a narrative. It tells of an event. The event is a very small one – the bite of a flea – but that is enough to make it a narrative.
Few, if any, scholars would dispute the necessity of at least one event for there to be narrative, but there are a number who require more than this. Some require at least two events, one after the other (Barthes, Rimmon-Kenan). And more than a few go even further, requiring that the events be causally related (Bal, Bordwell, Richardson). To both of these camps, my examples of narrative above would appear too impoverished to qualify. In my own view and that of still others (Genette, Smith), the field of narrative is so rich that it would be a mistake to become invested in a more restrictive definition that requires either more than one event or the sense of causal connection between events.