Halakhah sur Les Nombres 7:9

The commandment of carrying the Ark on the shoulder: That the priests (Kohanim) are commanded to carry the Ark on their shoulders when the People of Israel move it from one place to another, as it is stated (Numbers 7:9), "for the holy service is upon them, they shall carry on their shoulders." Rabbi Moshe ben Maimon (Maimonides), may his memory be blessed, wrote (Sefer HaMitzvot LaRambam, Mitzvot Ase 34) [that] even though this commandment came to the Levites, that was [only] at that time - meaning to say in the wilderness, due to the small number of Kohanim at that time. In [future] generations, however, the Kohanim were obligated in this commandment - and they shall carry it - as is elucidated from the Book of Joshua and the Book of Samuel.