The first observation of the decay B-0 -> D-0(D) over bar K-0(+)pi(-) is reported using proton-proton collision data corresponding to an integrated luminosity of 4.7 fb(-1) collected by the LHCb experiment in 2011, 2012 and 2016. The measurement is performed in the full kinematically allowed range of the decay outside of the D*(-) region. The ratio of the branching fraction relative to that of the control channel B-0 -> D-0<(DK+)-K-0 pi(-)+ is measured to be R = (14.2 +/- 1.1 +/- 1.0)%, where the first uncertainty is statistical and the second is systematic. The absolute branching fraction of B-0 -> D-0(D) over bar K-0(+)pi(- )decays is thus determined to be B(B-0 -> D-0(D) over bar K-0(+)pi(-)) = (3.50 +/- 0.27 +/- 0.26 +/- 0.30) x 10(-4), where the third uncertainty is due to the branching fraction of the control channel. This decay mode is expected to provide insights to spectroscopy and the charm-loop contributions in rare semileptonic decays.