The first observation of the decay B0→D0D¯0K+π- 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 B0→D∗-D0K+ 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 B0→D0D¯0K+π- decays is thus determined to be B(B0→D0D¯0K+π-)=(3.50±0.27±0.26±0.30)×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.