This paper presents a novel approach in Explainable AI (XAI), integrating contrastive explanations with differential privacy in clustering methods. For several basic clustering problems, including $k$-median and $k$-means, we give efficient differential private contrastive explanations that achieve essentially the same explanations as those that non-private clustering explanations can obtain. We define contrastive explanations as the utility difference between the original clustering utility and utility from clustering with a specifically fixed centroid. In each contrastive scenario, we designate a specific data point as the fixed centroid position, enabling us to measure the impact of this constraint on clustering utility under differential privacy. Extensive experiments across various datasets show our method's effectiveness in providing meaningful explanations without significantly compromising data privacy or clustering utility. This underscores our contribution to privacy-aware machine learning, demonstrating the feasibility of achieving a balance between privacy and utility in the explanation of clustering tasks.