Centralized training methods have shown promising results in MR image reconstruction, but privacy concerns arise when gathering data from multiple institutions. Federated learning, a distributed collaborative training scheme, can utilize multi-center data without the need to transfer data between institutions. However, existing federated learning MR image reconstruction methods rely on manually designed models which have extensive parameters and suffer from performance degradation when facing heterogeneous data distributions. To this end, this paper proposes a novel FederAted neUral archiTecture search approach fOr MR Image reconstruction (FedAutoMRI). The proposed method utilizes differentiable architecture search to automatically find the optimal network architecture. In addition, an exponential moving average method is introduced to improve the robustness of the client model to address the data heterogeneity issue. To the best of our knowledge, this is the first work to use federated neural architecture search for MR image reconstruction. Experimental results demonstrate that our proposed FedAutoMRI can achieve promising performances while utilizing a lightweight model with only a small number of model parameters compared to the classical federated learning methods.