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Measures to predict 30-day readmission are considered an important quality factor for hospitals as accurate predictions can reduce the overall cost of care by identifying high risk patients before they are discharged. While recent deep learning-based studies have shown promising empirical results on readmission prediction, several limitations exist that may hinder widespread clinical utility, such as (a) only patients with certain conditions are considered, (b) existing approaches do not leverage data temporality, (c) individual admissions are assumed independent of each other, which is unrealistic, (d) prior studies are usually limited to single source of data and single center data. To address these limitations, we propose a multimodal, modality-agnostic spatiotemporal graph neural network (MM-STGNN) for prediction of 30-day all-cause hospital readmission that fuses multimodal in-patient longitudinal data. By training and evaluating our methods using longitudinal chest radiographs and electronic health records from two independent centers, we demonstrate that MM-STGNN achieves AUROC of 0.79 on both primary and external datasets. Furthermore, MM-STGNN significantly outperforms the current clinical reference standard, LACE+ score (AUROC=0.61), on the primary dataset. For subset populations of patients with heart and vascular disease, our model also outperforms baselines on predicting 30-day readmission (e.g., 3.7 point improvement in AUROC in patients with heart disease). Lastly, qualitative model interpretability analysis indicates that while patients' primary diagnoses were not explicitly used to train the model, node features crucial for model prediction directly reflect patients' primary diagnoses. Importantly, our MM-STGNN is agnostic to node feature modalities and could be utilized to integrate multimodal data for triaging patients in various downstream resource allocation tasks.