Neural architecture search (NAS), which automates the architectural design process of deep neural networks (DNN), has attracted increasing attention. Multimodal DNNs that necessitate feature fusion from multiple modalities benefit from NAS due to their structural complexity; however, constructing an architecture for multimodal DNNs through NAS requires a substantial amount of labeled training data. Thus, this paper proposes a self-supervised learning (SSL) method for architecture search of multimodal DNNs. The proposed method applies SSL comprehensively for both the architecture search and model pretraining processes. Experimental results demonstrated that the proposed method successfully designed architectures for DNNs from unlabeled training data.