The Sarajevo Canton Interior Ministry said the protests would not be allowed because the rallies were not reported to the police 72 hours in advance, as required by law.
The ministry also said the police would resort to every measure envisioned by law if attempts were made to rally in front of the embassy.
The rallies protesting against the publication of caricatures of the Prophet Muhammad have been announced on a Bosnian Islamic web site.
Muslims already protested in Sarajevo on Wednesday, when Croatian, Danish, Norwegian and French paper flags were set on fire, an action condemned by Bosnian state officials and the deputy head of the Islamic community.