Magnetic resonance imaging (MRI) is one of the noninvasive imaging modalities that can produce high-quality images. However, the scan procedure is relatively slow, which causes patient discomfort and motion artifacts in images. Accelerating MRI hardware is constrained by physical and physiological limitations. A popular alternative approach to accelerated MRI is to undersample the k-space data. While undersampling speeds up the scan procedure, it generates artifacts in the images, and advanced reconstruction algorithms are needed to produce artifact-free images. Recently deep learning has emerged as a promising MRI reconstruction method to address this problem. However, straightforward adoption of the existing deep learning neural network architectures in MRI reconstructions is not usually optimal in terms of efficiency and reconstruction quality. In this work, MRI reconstruction from undersampled data was carried out using an optimized neural network using a novel evolutionary neural architecture search algorithm. Brain and knee MRI datasets show that the proposed algorithm outperforms manually designed neural network-based MR reconstruction models.