Mercedes said they had to make the change after the 2008 Formula One world champion hit a kerb in final practice and damaged his car's suspension.
Hamilton then qualified fourth quickest and so will start from ninth.
Hamilton took the top slot in China last weekend, his first pole for the team he joined from McLaren at the end of 2012.
"Lewis's gearbox will be changed before qualifying following the incident in P3 ... Lewis will incur a five-place grid penalty as a result," Mercedes said on Twitter before qualifying.
Red Bull's Mark Webber has a three-place penalty in Bahrain for causing a collision in China and will start from seventh after qualifying fifth fastest while Sauber's Esteban Gutierrez has a five-place sanction for driving into the back of Adrian Sutil's Force India in the same race and will start from the back of the grid.
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