This paper reports the first ATLAS measurement of the B-s(0) -> mu mu effective lifetime. The measurement is based on the data collected in 2015-2016, amounting to 26.3 fb(-1) of 13TeV LHC proton-proton collisions. The proper decay-time distribution of 58 +/- 13 background-subtracted signal candidates is fit with simulated signal templates parameterised as a function of the B-s(0) effective lifetime, with statistical uncertainties extracted through a Neyman construction. The resulting effective measurement of the B-s(0) -> mu mu lifetime is 0.99(-0.07)(+0.42) (stat.) +/- 0.17 (syst.) ps and it is found to be consistent with the Standard Model.