Black-box machine learning models are used in critical decision-making domains, giving rise to several calls for more algorithmic transparency. The drawback is that model explanations can leak information about the training data and the explanation data used to generate them, thus undermining data privacy. To address this issue, we propose differentially private algorithms to construct feature-based model explanations. We design an adaptive differentially private gradient descent algorithm, that finds the minimal privacy budget required to produce accurate explanations. It reduces the overall privacy loss on explanation data, by adaptively reusing past differentially private explanations. It also amplifies the privacy guarantees with respect to the training data. We evaluate the implications of differentially private models and our privacy mechanisms on the quality of model explanations.