Reference: Taqyeed ash-Shawaarid min al-Qawaa.id wal-Fawaa.id – Page 301
It is permissible for a disbeliever to enter Madeenah based upon the evidence that when Thumaamah ibn Athaal took the horses of the companions, they brought him [back] and tied him to one of the pillars of the Masjid [an-Nabawee]. In contrast, the disbeliever is not permitted to enter Makkah, because of the statement of Allaah (Subhaanahu wa Ta’aala):
The scholars have even said that if a delegation of the disbelievers came to see the leader of the Muslims whilst he was in Makkah, then they are not to enter Makkah, rather, he is to go out [of Makkah] to meet them. And this is from the differences between Makkah and Madeenah.