Warner was struck by a Mitchell Johnson delivery while batting in the nets at Perth, suffering a minor left thumb fracture and ruling him out of the matches on Friday and Sunday at the WACA.
"While the fracture is very minor, it is not worth taking any risks," physiotherapist Kevin Sims said.
"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."
After the five-match one-day series against West Indies followed by a Twenty20 International, Australia will tour India for a four-Test series beginning on February 22.