Prophet Muhammad (PBUH) is a prophet to the whole world and not only to the Muslims.
It is about 100 years that there has emerged in our books a mistake and that is the phrase of ‘the Prophet of Islam’. Before this last century, in all books, whether in Persian or Arabic, wherever a mention of the Prophet (PBUH) has been made, he has been introduced as the prophet of God. The Quran also introduces him as the Prophet of God: "There is certainly a good exemplar for you in the Apostle of Allah". 
Say, ‘O mankind! I am the Apostle of Allah to you all, [of Him] to whom belongs the kingdom of the heavens and the earth. There is no god except Him. He gives life and brings death.’ So have faith in Allah and His Apostle, the untaught prophet, who has faith in Allah and His words, and follow him so that you may be guided. 
In the books of Hadith also, he is mentioned as the Prophet of God. Prophet Muhammad (PBUH) is a prophet to the whole world and not only to the Muslims. Most likely, this term has been coined by the orientalists either unintentionally or intentionally to imply that he belongs to only one group of people and therefore, direct attentions away from universality of his divine mission. Then, it has found its way into the works of Muslim authors.
 (33:21) لَّقَدْ كَانَ لَكُمْ فِي رَسُولِ اللَّـهِ أُسْوَةٌ حَسَنَةٌ
 (7:158) قُلْ يَا أَيُّهَا النَّاسُ إِنِّي رَسُولُ اللَّـهِ إِلَيْكُمْ جَمِيعًا الَّذِي لَهُ مُلْكُ السَّمَاوَاتِ وَالْأَرْضِ ۖ لَا إِلَـٰهَ إِلَّا هُوَ يُحْيِي وَيُمِيتُ ۖ فَآمِنُوا بِاللَّـهِ وَرَسُولِهِ النَّبِيِّ الْأُمِّيِّ الَّذِي يُؤْمِنُ بِاللَّـهِ وَكَلِمَاتِهِ وَاتَّبِعُوهُ لَعَلَّكُمْ تَهْتَدُونَ