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We investigate the possibility whether the tensions with SM expectations observed in several b→sℓℓ transitions, including hints for lepton flavour non-universality, could be due to the decay of B into a new light resonance. We find that qualitative agreement with the data can be obtained with a light vector resonance dominantly decaying invisibly. This scenario predicts a shift in the muon anomalous magnetic moment that could explain the long-standing discrepancy. The most stringent constraint comes from searches for B decays with missing energy. A striking prediction is a strong q2 dependence of the lepton flavour universality ratios RK and RK⁎ that should allow to clearly confirm or rule out this possibility experimentally. We also comment on the possible connection of the invisible decay product with Dark Matter.