The Frenchman had charged from the back of the field to finish sixth, but on the last lap he encountered an issue with his gearbox - which would have forced him out of the race if it had struck earlier.
Analysis of the gearbox by Lotus has shown that it will need replacing, which means he will face a grid drop in Hockenheim.
Lotus technical director James Allison said: "It was a gearbox problem and we are very fortunate that Romain didn't have the problem earlier in the race.
"Unfortunately for Romain it means he'll take a five place grid penalty at Hockenheim, but he certainly showed at Silverstone that dropping down the order won't stop him challenging at the sharp end."
Although Lotus has shown good speed in races, the grid penalty will be a big blow because the team has often found it chances on Sunday compromised by poor qualifying performances.
Before news of his penalty, Grosjean himself reckoned that the team will only realistically have a shout at victory if it can qualify on the first two rows.
"We need to put everything together," he said. "We've been saying that for a while now, but I'm sure it's going to come. If we can manage a good qualifying - in the front two rows - then I'm sure we can get the win."