Various saliency map methods have been proposed to interpret and explain predictions of deep learning models. Saliency maps allow us to interpret which parts of the input signals have a strong influence on the prediction results. However, since a saliency map is obtained by complex computations in deep learning models, it is often difficult to know how reliable the saliency map itself is. In this study, we propose a method to quantify the reliability of a saliency region in the form of p-values. Our idea is to consider a saliency map as a selected hypothesis by the trained deep learning model and employ the selective inference framework. The proposed method provably provides a valid p-value for the detected salient region, i.e., we can provably control the false positive rate of the detected salient region. We demonstrate the validity of the proposed method through numerical examples in synthetic and real datasets. Furthermore, we develop a Keras-based framework for conducting the proposed selective inference for a wide class of CNNs without additional implementation cost.