The 29-year-old showed off the design, which is a tribute to Germany's World Cup triumph in Brazil, earlier this week.
However, due to a breach of intellectual property rights, Rosberg is not permitted to display the trophy, but can have the national flag and four stars to represent the number of times that Germany have won the tournament.
"We cannot allow a commercially branded helmet to feature the trophy as this would jeopardise the rights of our commercial affiliates," BBC Sport quotes a FIFA statement as saying.
"We appreciate Nico Rosberg's desire to congratulate the German team and have therefore been in discussions with the Rosberg team to attempt to find a solution, whereby he is still able to show his support for Germany without using FIFA intellectual property in a commercial context."
Rosberg will take part in his home Grand Prix at Hockenheim after signing a new long-term deal with Mercedes yesterday.