A processor includes a plurality of packed data registers, a decode unit, and an execution unit. The decode unit is to decode a three-dimensional (3D) Morton coordinate conversion instruction. The 3D Morton coordinate conversion instruction to indicate a source packed data operand that is to include a plurality of 3D Morton coordinates, and to indicate one or more destination storage locations. The execution unit is coupled with the packed data registers and the decode unit. The execution unit, in response to the decode unit decoding the 3D Morton coordinate conversion instruction, is to store one or more result packed data operands in the one or more destination storage locations. The one or more result packed data operands are to include a plurality of sets of three 3D coordinates. Each of the sets of the three 3D coordinates is to correspond to a different one of the 3D Morton coordinates.