Hamilton crossed the chequered flag in 11th place in Hockenheim on Sunday.
However, both Alfa Romeo drivers, Kimi Raikkonen and Antonio Giovinazzi, who finished seventh and eighth respectively, were slapped with 30 second penalties.
It was said the pair fell foul of regulations concerning clutch settings at the start of the race which enabled them to shoot off the grid quicker.
The punishment meant Hamilton rose to ninth and Williams scored their first point of the campaign as Robert Kubica was promoted to 10th.
But Alfa Romeo boss Frederic Vasseur has launched an appeal to get the decision overturned.
He claims to have evidence which proves his side did not try to gain an advantage.
“Alfa Romeo Racing lodged an appeal against the decision No. 56 and 57 of the Stewards of the 2019 German Grand Prix,” a statement read this afternoon.
Vasseur explained after the race that he would be challenging the decision.
“The situation arose during the laps we spent behind the safety car ahead of the standing start,” he said.
“We suffered a dysfunction of the clutch that was beyond our control and we will further investigate the issue.
“We respect the FIA’s process and the stewards’ work, but will appeal this decision as we believe we have the grounds and evidence to have it overturned.
“In this regard, we will be in touch with the FIA soon.”
Hamilton’s two points took him 41 clear of Mercedes team-mate Valtteri Bottas at the top of the standings.
It also left Max Verstappen, who won the German Grand Prix, 63 points in his wake.
But those deficits could be cut if Alfa Romeo are successful in their appeal.