A sample of 114 ± 11 B 0 s → J / ψ K − π + signal events obtained with 0.37     fb − 1 of p p collisions at √ s = 7     TeV collected by the LHCb experiment is used to measure the branching fraction and polarization amplitudes of the B 0 s → J / ψ ¯¯¯¯ K * 0 decay, with ¯¯¯¯ K * 0 → K − π + . The K − π + mass spectrum of the candidates in the B 0 s peak is dominated by the ¯¯¯¯ K * 0 contribution. Subtracting the nonresonant K − π + component, the branching fraction of B 0 s → J / ψ ¯¯¯¯ K * 0 is ( 4.4 + 0.5 − 0.4 ± 0.8 ) × 10 − 5 , where the first uncertainty is statistical and the second is systematic. A fit to the angular distribution of the decay products yields the K * 0 polarization fractions f L = 0.50 ± 0.08 ± 0.02 and f ∥ = 0.19 + 0.10 − 0.08 ± 0.02 .