Intelligent behavior is an emergent phenomenon observed in biological organisms across all scales. It describes the cooperative behavior of low complexity entities to accomplish complex tasks, which exceed their individual capabilities. This property is particularly important for the Internet of Bio-Nano Things (IoBNT), which consists of Bio-Nano Things (BNTs) used in the human body, where they face many restrictions, such as bio-compatibility and size constraints. In this paper, we present a novel BNT-architecture, called Molecular Nano Neural Networks (M3N), which allows the implementation of intelligence on the micro-/nano-scale. The proposed structure consists of compartments (low complexity entities) that are connected to each other to form a network. Based on reaction and diffusion of molecules in and between connected compartments, this network mimics an artificial neural network, which is an important step towards  artificial intelligence in the IoBNT. We provide design guidelines for the proposed M3N and successfully validate it by applying a regression and classification task.