Semiconductor nanopyramids (NPs) provide advantages in the development of novel functional optoelectronic devices due to their unique size-dependent properties. Here we demonstrate a new method for the fabrication of selectively self-assembled single-crystalline GaN NPs on the m-plane of periodically strained GaN/InGaN multiquantum disks embedded in the middle of GaN nanorods. The GaN NPs, which have ~100 nm diameters and heights, are observed by scanning electron microscopy and their crystalline structure is confirmed by high-resolution transmission electron microscopy. Experimental analysis directly reveals the strain distribution along the growth direction of the NPs. Cathodoluminescence measurements on a single NP show that its emission energy redshifts compared with that of bulk GaN, corroborating the results showing the formation of tensile strain in the NP. Observations of the uniform distribution and localization of these NPs show the possibility of further tuning their size and density by controlling periodically strained nanorod surfaces.