For any positive integer r, the r-Fubini number with parameter n, denoted by F_n,r, is equal to the number of ways that the elements of a set with n + r elements can be weakly ordered such that the r least elements are in distinct orders. In this article we focus on the sequence of residues of the r-Fubini numbers modulo an arbitrary positive integer s and show that this sequence is periodic and then, exhibit how to calculate its period length.