Usually the medieval European universities are distinguished by
not being primarily religious institutions, although there have been objections to this definition. Otherwise, several older madrasas remain in operation, the oldest being the University of al-Qarawiyyin in Fez, Morocco (847), which is listed as the world's oldest university by e.g. the
Guinness Book of World Records:
https://en.wikipedia.org/wiki/University_of_al-Qarawiyyin
Surprisingly, there are some schools for adolescents in England which are even older, the oldest dating to 597:
https://en.wikipedia.org/wiki/The_King%27s_School,_Canterbur...
That the oldest continuously operating institutions in the world are mostly in England (schools), Japan (hotels) and the desert mountains of North Africa (madrasas and St. Catherine's Monastery) is likely a consequence of "splendid isolation". Nobody is quite sure how old the government of Haida Gwaii is.