Fuzzy congruence relations on algebras are defined in [3], and discussed in [2, 4] and [5]. Fuzzy groupoids are considered in [1, 5] and [2]. In this paper, we define a weak fuzzy congruence relation on a groupoid, and we prove that this relation uniquely determines a fuzzy groupoid on the same algebra. Starting with a weak fuzzy congruence relation $\bar{\rho}$ on a groupoid $(S,.)$ and using the decomposition of a fuzzy set defined in [2], we get two collections of fuzzy sets (on $S$, and on $S^2$, respectively). We prove that the first collection consists of the fuzzy groupoids on $(S,.)$, and that in the second are the fuzzy congruence relations on these groupoids.