The embassy attacks in Damascus were the most violent in a day of demonstrations by Muslims across the Middle East, Europe and Asia.
In Gaza, Palestinians marched through the streets, storming European buildings and burning German and Danish flags.
Protesters smashed the windows of the German cultural centre and threw stones at the European Commission building, police said.
The leader of the Palestinian group Hamas called the cartoons "an unforgivable insult" which merited punishment by death.
Hundreds of Iraqis rallied to demand an apology from the European Union.
Pakistan summoned the envoys of nine Western countries to register protests.
Demonstrators took to the streets in Denmark and Britain to voice their anger.
The protests have erupted over 12 caricatures of the Prophet Mohammad first published in Denmark's Jyllands-Posten in September and reprinted by European media in the past week.
Denmark's Prime Minister Anders Fogh Rasmussen has said repeatedly he cannot apologise for his country's free press.
But other European leaders have tried to calm the storm.
Denmark and Norway have advised their citizens to leave Syria without delay.