A radar echo sequence which includes N frames plays a crucial role in monitoring precipitation clouds and serves as the foundation for accurate precipitation forecasting. To predict future frames, spatiotemporal models are used to leverage historical radar echo sequences. The spatiotemporal information combining both temporal and spatial information is derived from radar echo sequence. The spatiotemporal information reveals the changing trend of intensity in the echo region over time. Dynamic variation information extracted in radar echo maps mainly consists of nonstationary information and spatiotemporal information. However, the changing trends at different locations within the precipitation cloud are different, so the significance of the spatiotemporal information should be different. The current precipitation forecasting model, Memory In Memory (MIM), has the capability to store the nonstationary information derived from radar echo maps. However, the MIM falls short in discerning the significance of the spatiotemporal information extracted from these maps. To address this limitation, we propose a novel model, SAMM‐MIM (self‐attention memory module‐MIM), which regulates the generation of hidden states and spatiotemporal memory states using a SAMM. The proposed SAMM uses the self‐attention mechanism and a series of gate mechanisms to concentrate on significant spatiotemporal information, learn changing trends in the echo region, and output predictive information. The predictive information which is stored in hidden states contains predictions of the changing trends of dynamic variation information. Experimental evaluation on a dataset of radar data from Qingdao, China, demonstrates that SAMM‐MIM achieves superior prediction performance compared with other spatiotemporal sequence models, as indicated by improved scores on mean squared error, critical success index, and missing alarm rate metrics.