Multimodal recommender systems (MRS) improve recommendation performance by integrating complementary semantic information from multiple modalities. However, the assumption of complete multimodality rarely holds in practice due to missing images and incomplete descriptions, hindering model robustness and generalization. To address these challenges, we introduce a novel method called \textbf{I$^3$-MRec}, which uses \textbf{I}nvariant learning with \textbf{I}nformation bottleneck principle for \textbf{I}ncomplete \textbf{M}odality \textbf{Rec}ommendation. To achieve robust performance in missing modality scenarios, I$^3$-MRec enforces two pivotal properties: (i) cross-modal preference invariance, ensuring consistent user preference modeling across varying modality environments, and (ii) compact yet effective multimodal representation, as modality information becomes unreliable in such scenarios, reducing the dependence on modality-specific information is particularly important. By treating each modality as a distinct semantic environment, I$^3$-MRec employs invariant risk minimization (IRM) to learn preference-oriented representations. In parallel, a missing-aware fusion module is developed to explicitly simulate modality-missing scenarios. Built upon the Information Bottleneck (IB) principle, the module aims to preserve essential user preference signals across these scenarios while effectively compressing modality-specific information. Extensive experiments conducted on three real-world datasets demonstrate that I$^3$-MRec consistently outperforms existing state-of-the-art MRS methods across various modality-missing scenarios, highlighting its effectiveness and robustness in practical applications.

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