Machine unlearning (MU) has gained significant attention as a means to remove specific data from trained models without requiring a full retraining process. While progress has been made in unimodal domains like text and image classification, unlearning in multimodal models remains relatively underexplored. In this work, we address the unique challenges of unlearning in CLIP, a prominent multimodal model that aligns visual and textual representations. We introduce CLIPErase, a novel approach that disentangles and selectively forgets both visual and textual associations, ensuring that unlearning does not compromise model performance. CLIPErase consists of three key modules: a Forgetting Module that disrupts the associations in the forget set, a Retention Module that preserves performance on the retain set, and a Consistency Module that maintains consistency with the original model. Extensive experiments on the CIFAR-100 and Flickr30K datasets across four CLIP downstream tasks demonstrate that CLIPErase effectively forgets designated associations in zero-shot tasks for multimodal samples, while preserving the model's performance on the retain set after unlearning.