Uncertainty estimation is an important research area to make deep neural networks (DNNs) more trustworthy. While extensive research on uncertainty estimation has been conducted with unimodal data, uncertainty estimation for multimodal data remains a challenge. Neural processes (NPs) have been demonstrated to be an effective uncertainty estimation method for unimodal data by providing the reliability of Gaussian processes with efficient and powerful DNNs. While NPs hold significant potential for multimodal uncertainty estimation, the adaptation of NPs for multimodal data has not been carefully studied. To bridge this gap, we propose Multimodal Neural Processes (MNPs) by generalising NPs for multimodal uncertainty estimation. Based on the framework of NPs, MNPs consist of several novel and principled mechanisms tailored to the characteristics of multimodal data. In extensive empirical evaluation, our method achieves state-of-the-art multimodal uncertainty estimation performance, showing its appealing robustness against noisy samples and reliability in out-of-distribution detection with faster computation time compared to the current state-of-the-art multimodal uncertainty estimation method.