Machine Unlearning is the process of removing specific training data samples and their corresponding effects from an already trained model. It has significant practical benefits, such as purging private, inaccurate, or outdated information from trained models without the need for complete re-training. Unlearning within a multimodal setting presents unique challenges due to the intrinsic dependencies between different data modalities and the expensive cost of training on large multimodal datasets and architectures. Current approaches to machine unlearning have not fully addressed these challenges. To bridge this gap, we introduce MMUL, a machine unlearning approach specifically designed for multimodal data and models. MMUL formulates the multimodal unlearning task by focusing on three key properties: (a): modality decoupling, which effectively decouples the association between individual unimodal data points within multimodal inputs marked for deletion, rendering them as unrelated data points within the model's context, (b): unimodal knowledge retention, which retains the unimodal representation capability of the model post-unlearning, and (c): multimodal knowledge retention, which retains the multimodal representation capability of the model post-unlearning. MMUL is efficient to train and is not constrained by the requirement of using a strongly convex loss. Experiments on two multimodal models and four multimodal benchmark datasets, including vision-language and graph-language datasets, show that MMUL outperforms existing baselines, gaining an average improvement of +17.6 points against the best-performing unimodal baseline in distinguishing between deleted and remaining data. In addition, MMUL can largely maintain pre-existing knowledge of the original model post unlearning, with a performance gap of only 0.3 points compared to retraining a new model from scratch.