Accurate and timely estimation of tropical cyclone (TC) wind radii is significant for characterizing wind structure, disaster prevention, and mitigation. The existing methods have not sufficiently considered and utilized multimodal (i.e., multisource heterogeneous) data for wind radii estimation. Meanwhile, complete modalities (i.e., all used modalities) can hardly be available simultaneously, especially in real-time monitoring scenarios, which restricts the applicability of multimodal estimation models. It is challenging to maintain the accuracy of wind radii estimates when confronted with the issue of missing-modality. Therefore, to address these issues, this article aims to achieve robust TC wind radii estimation under both conditions with complete modalities and missing-modality. We first present a multimodal fusion network, MT-TCNet, for estimating TC wind radii under conditions with complete modalities. MT-TCNet benefits from multimodal data including satellite infrared (IR) images, reanalysis of wind fields, and the physical parameter maximum sustained wind (MSW) speed. MSW, which reflects TC intensity, is incorporated to embed the implicit relationship between TC intensity and wind radii. It is capable of providing superior and robust wind radii estimates in scenarios without time constraints, and can be used to generate long-term historical results. Furthermore, this article proposes MT-TCNet-Distill to alleviate the issue of missing-modality caused by delays in ERA5 reanalysis wind fields through generalized distillation and missing modality imputation. MT-TCNet-Distill broadens the applicability of MT-TCNet, which heavily relies on reanalysis data, enabling robust wind radii estimation in real-time scenarios. Comprehensive experiments demonstrate the superior performance of MT-TCNet and MT-TCNet-Distill compared to state-of-the-art methods.