Privacy preservation in AI is crucial, especially in healthcare, where models rely on sensitive patient data. In the emerging field of machine unlearning, existing methodologies struggle to remove patient data from trained multimodal architectures, which are widely used in healthcare. We propose Forget-MI, a novel machine unlearning method for multimodal medical data, by establishing loss functions and perturbation techniques. Our approach unlearns unimodal and joint representations of the data requested to be forgotten while preserving knowledge from the remaining data and maintaining comparable performance to the original model. We evaluate our results using performance on the forget dataset, performance on the test dataset, and Membership Inference Attack (MIA), which measures the attacker's ability to distinguish the forget dataset from the training dataset. Our model outperforms the existing approaches that aim to reduce MIA and the performance on the forget dataset while keeping an equivalent performance on the test set. Specifically, our approach reduces MIA by 0.202 and decreases AUC and F1 scores on the forget set by 0.221 and 0.305, respectively. Additionally, our performance on the test set matches that of the retrained model, while allowing forgetting. Code is available at https://github.com/BioMedIA-MBZUAI/Forget-MI.git