In sketched clustering, a dataset of T samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity independent of T. For the sketching methodology recently proposed by Keriven, et al., which can be interpreted as a random sampling of the empirical characteristic function, we propose a sketched clustering algorithm based on approximate message passing. Numerical experiments suggest that our approach is more efficient than the state-of-the-art sketched clustering algorithm "CL-OMPR" (in both computational and sample complexity) and more efficient than k-means++ when T is large.