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Although a vast body of literature relates to image segmentation methods that use deep neural networks (DNNs), less attention has been paid to assessing the statistical reliability of segmentation results. In this study, we interpret the segmentation results as hypotheses driven by DNN (called DNN-driven hypotheses) and propose a method by which to quantify the reliability of these hypotheses within a statistical hypothesis testing framework. Specifically, we consider a statistical hypothesis test for the difference between the object and background regions. This problem is challenging, as the difference would be falsely large because of the adaptation of the DNN to the data. To overcome this difficulty, we introduce a conditional selective inference (SI) framework -- a new statistical inference framework for data-driven hypotheses that has recently received considerable attention -- to compute exact (non-asymptotic) valid p-values for the segmentation results. To use the conditional SI framework for DNN-based segmentation, we develop a new SI algorithm based on the homotopy method, which enables us to derive the exact (non-asymptotic) sampling distribution of DNN-driven hypothesis. We conduct experiments on both synthetic and real-world datasets, through which we offer evidence that our proposed method can successfully control the false positive rate, has good performance in terms of computational efficiency, and provides good results when applied to medical image data.