The packing chromatic numberχρ(G) of a graph G is the smallest integer k for which there exists a vertex coloring Γ:V(G)→{1,2,…,k} such that any two vertices of color i are at distance at least i+1. For g∈{6,8,12}, (q+1,g)-Moore graphs are (q+1)-regular graphs with girth g which are the incidence graphs of a symmetric generalized g∕2-gons of order q. In this paper we study the packing chromatic number of a (q+1,g)-Moore graph G. For g=6 we present the exact value of χρ(G). For g=8, we determine χρ(G) in terms of the intersection of certain structures in generalized quadrangles. For g=12, we present lower and upper bounds for this invariant when q≥9 is an odd prime power.