Stewards handed the five times world champion, who had qualified second behind Ferrari's Charles Leclerc, a three-place drop for impeding Alfa Romeo's Kimi Raikkonen in qualifying.
That eventually translated into fourth place on the provisional grid, due to another penalty being applied first to Haas's Kevin Magnussen.
The sanction means Red Bull's Max Verstappen, last year's race winner, moves up to form a front row of 21-year-olds.
"Totally deserved the penalty today and have no problem accepting it," Hamilton said on Instagram.
"Was a mistake on my behalf and I take full responsibility for it. It wasn't intentional. Anyway, tomorrow is another day and an opportunity to rise.
"These things are sent to try us. We all have to push through whatever it is we are up against, whether it's right or wrong, just continue to believe in yourself!," he added. "We have the power to overcome obstacles even when they appear too large a task."
Hamilton was also handed one penalty point, his first of the 12 months period.
The Briton is leading team mate Valtteri Bottas by 36 points after winning the last four races and six out of eight. Mercedes have won 10 races in a row in total, including the last two of 2018.
Bottas will start in third place, having qualified fourth. The Finn had been on pole in Austria for the two previous years, winning in 2017.
(Reporting by Alan Baldwin in London, editing by Toby Davis/Clare Lovell)
