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Abstract We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) A N−1 and D N theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS 7 × S 4 and AdS 7 × S 4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R 4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.