While biological neural networks develop from compact genomes using relatively simple rules, modern artificial neural architecture search methods mostly involve explicit and routine manual work. In this paper, we introduce MorphoNAS (Morphogenetic Neural Architecture Search), a system able to deterministically grow neural networks through morphogenetic self-organization inspired by the Free Energy Principle, reaction-diffusion systems, and gene regulatory networks. In MorphoNAS, simple genomes encode just morphogens dynamics and threshold-based rules of cellular development. Nevertheless, this leads to self-organization of a single progenitor cell into complex neural networks, while the entire process is built on local chemical interactions. Our evolutionary experiments focused on two different domains: structural targeting, in which MorphoNAS system was able to find fully successful genomes able to generate predefined random graph configurations (8-31 nodes); and functional performance on the CartPole control task achieving low complexity 6-7 neuron solutions when target network size minimization evolutionary pressure was applied. The evolutionary process successfully balanced between quality of of the final solutions and neural architecture search effectiveness. Overall, our findings suggest that the proposed MorphoNAS method is able to grow complex specific neural architectures, using simple developmental rules, which suggests a feasible biological route to adaptive and efficient neural architecture search.