This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between the microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. The proposed approach has been evaluated using real data recordings where the distance of the close-by microphones are estimated based on the coherence model of an enclosure diffuse noise field. The results confirm that the proposed algorithm outperforms the state-of-the-art calibration techniques.