McLaren will fit new gearboxes to both cars but Hamilton will not be penalised because he failed to finish the race.
Hamilton announced last week that this would be his last season for McLaren after signing a deal with Mercedes.
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"This is a great disappointment for Jenson and the team," said McLaren technical director Paddy Lowe. "On the positive side, we have understood and completely resolved the issue, allowing both drivers to compete with confidence for podium positions."
Button, the 2009 world champion, is chasing back-to-back wins
He had been "convinced" he could "fight for victory" in Japan but that view might change in light of the penalty.
He is currently sixth in the title race and 75 points adrift of championship leader Fernando Alonso with six races remaining.
Rules dictate that each driver is required to use the same gearbox for five consecutive events. If the team has to use a replacement gearbox outside of this period, then the driver drops five places on the grid.
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