Mitchell Johnson struck the left-hander with a delivery during a practice session in Perth ahead of the February games against the Twenty20 world champions.
Team physiotherapist Kevin Sims said: "While the fracture is very minor, it is not worth taking any risks.
"The injury will keep him out of at least the next two matches against West Indies. We'll assess how he is progressing after that to determine his availability for the remainder of the series."
Usman Khawaja has been called into the squad as cover for Warner.