Rosberg finished second in the race behind his team mate Lewis Hamilton and ahead of Red Bull’s Max Verstappen, but in the closing laps he was helped by his Mercedes engineers when hit by a gearbox problem.
Over the radio he was told to change a chassis setting when the problem struck and also to not drive with seventh gear and instead bypass to eighth.
A statement issued by the FIA said that while some of the instructions Mercedes gave him were allowed, other parts of the advice were illegal.
“Having considered the matter extensively, the Stewards determined that the team gave some instructions to the driver that were specifically permitted under Technical Directive 014-16,” it said.
“However, the Stewards determined that the team then went further and gave instructions to the driver that were not permitted under the Technical Directive, and were in Breach of Art. 27.1 of the Sporting Regulations, that the driver must drive the car alone and unaided.”
The penalty means that Rosberg moves down to third place promoting Max Verstappen to second.
In the drivers’ championship Rosberg now lies just a single point ahead of Hamilton.