Existing methods for few-shot speaker identification (FSSI) obtain high accuracy, but their computational complexities and model sizes need to be reduced for lightweight applications. In this work, we propose a FSSI method using a lightweight prototypical network with the final goal to implement the FSSI on intelligent terminals with limited resources, such as smart watches and smart speakers. In the proposed prototypical network, an embedding module is designed to perform feature grouping for reducing the memory requirement and computational complexity, and feature interaction for enhancing the representational ability of the learned speaker embedding. In the proposed embedding module, audio feature of each speech sample is split into several low-dimensional feature subsets that are transformed by a recurrent convolutional block in parallel. Then, the operations of averaging, addition, concatenation, element-wise summation and statistics pooling are sequentially executed to learn a speaker embedding for each speech sample. The recurrent convolutional block consists of a block of bidirectional long short-term memory, and a block of de-redundancy convolution in which feature grouping and interaction are conducted too. Our method is compared to baseline methods on three datasets that are selected from three public speech corpora (VoxCeleb1, VoxCeleb2, and LibriSpeech). The results show that our method obtains higher accuracy under several conditions, and has advantages over all baseline methods in computational complexity and model size.