Hamilton performed a practice start outside of the designated area as he left the pits.
The penalties were due to be added on at the end of the race.
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It means the British driver will have to win by more than 10 seconds if he is to match Michael Schumacher’s record of 91 wins.
BREAKING: Lewis Hamilton is under investigation by the race stewards for a practice start outside of the designated area #RussianGP 🇷🇺 #F1 pic.twitter.com/Gw3NoKgvwe
— Formula 1 (@F1) September 27, 2020
The six-time world champion started from pole position in Sochi after claiming the 96th pole of his career on Saturday.
Hamilton retained his lead in the early stages of the race after a clean getaway following a safety car period.