Both drivers hit trouble during Saturday's morning's final free practice session in Melbourne.
The pair managed just two installation laps each before their teams discovered the gearboxes needed changing.
Under the 2014 F1 regulations, gearboxes are now supposed to last for six consecutive events.
The changes mean that both drivers will be moved back five places on the grid.
For Bottas the news is a particular blow because he had headed in to the weekend as a strong contender for a podium finish and had been a comfortable top 10 runner in practice on Friday.
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