We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small and roughly equal subgraphs and constructs a distributed data structure containing shortest distances within each of those subgraphs and between their boundary vertices. For a planar graph with $n$ vertices, that data structure needs $O(n)$ storage per processor and allows queries to be answered in $O(n^{1/4})$ time.