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We report on a universal method to measure the genuine indistinguishability of n photons—a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer with N=2n modes, leading to a quantum interference fringe whose visibility is a direct measurement of the genuine n-photon indistinguishability. We experimentally demonstrate this technique for an eight-mode integrated interferometer fabricated using femtosecond laser micromachining and four photons from a quantum dot single-photon source. We measure a four-photon indistinguishability up to 0.81±0.03. This value decreases as we intentionally alter the photon pairwise indistinguishability. The low-depth and low-loss multiport interferometer design provides an original path to evaluate the genuine indistinguishability of resource states of increasing photon number.