In general, no, but the current government does not allow most of them in due to the school of thought they follow.
Reason for Asking the Question
Either non-Muslims would genuinely like to visit Makkah and Madinah to see what it is like or some people who hate Islam try to use this as an argument that Islam is unfair.
What the Qur’an Said
Allah says, “Believers, the idolaters are impure, so do not let them come near the Sacred House after this year.’ [9:28] This refers to the pilgrimage and not in general.
What the Scholars Said
Imam Abu Hanifah said that non-Muslims are only prevented from performing Hajj or Umrah. They are not prevented from visiting Makkah, Madinah, or any other mosque. (Tafsir Mazhari 5:232)
Shaykh Mustafa Umar