The Mercedes driver, who won from 14th on the grid, was suspected of having illegally crossed a line separating the entry from the track when he hurriedly changed his mind about pitting during a safety car period.
After summoning Hamilton, the Hockenheim stewards found the 33-year-old guilty of breaking the regulations but opted to hand him a reprimand rather than a time penalty.
The ruling took into account that the driver and team admitted their mistake; that the offence was during a safety car period, when the speed of cars on track is controlled; and that the manoeuvre did not endanger any other drivers and was "executed in a safe way".
"It's the most emotional day, up and down," Hamilton told Sky Sports News.
"No-one ever wants to go and see the stewards, they have the hardest job because every scenario is always different, but this has just been an unbelievable day."
Hamilton's win gave him a 17-point championship lead over rival Sebastian Vettel.