The penalty, Button's second in a row after a 15 place drop in Canada, will translate in part into time penalties during the race due to the impossibility of the Briton dropping any further than 20th.
In a farcical turn of events, triggered by regulations that stipulate drivers must make four engines last the entire season or pay a penalty, Button and team mate Fernando Alonso will theoretically be demoted 45 places between them.
The Spaniard was handed a 20 place penalty on Friday after McLaren changed his engine and two of the five components that make up the troubled Honda V6 turbo hybrid power unit.
Alonso, a double world champion who left Ferrari at the end of 2014, has yet to score a point in seven races this season.
Button had been resigned to penalties when the 2009 champion spoke to reporters after suffering a "massive" power failure in second Friday practice.
"I'm probably going to start at the back," he said. "And then Sunday, who knows? With penalties, you sort of really need a safety car to bring you back into the game. Hopefully that will be the case and we can race."
In a further complication for fans struggling to keep up with the engine implications, Red Bull's Australian Daniel Ricciardo and Russian Daniil Kvyat also face 10 place grid drops from wherever they qualify.
The situation, at Red Bull's home circuit, has ratcheted up the criticism of engine partners Renault from the frustrated former champions.
(Reporting by Alan Baldwin, editing by...)
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