The first observation of the decay B 0 s → ¯¯¯ D 0 K − π + is reported. The analysis is based on a data sample, corresponding to an integrated luminosity of 1.0     fb − 1 of p p collisions, collected with the LHCb detector. The branching fraction relative to that of the topologically similar decay B 0 → ¯¯¯ D 0 π + π − is measured to be B ( B 0 s → ¯¯¯ D 0 K − π + ) B ( B 0 → ¯¯¯ D 0 π + π − ) = 1.18 ± 0.05 ( stat ) ± 0.12 ( syst ) . In addition, the relative branching fraction of the decay B 0 → ¯¯¯ D 0 K + π − is measured to be B ( B 0 → ¯¯¯ D 0 K + π − ) B ( B 0 → ¯¯¯ D 0 π + π − ) = 0.106 ± 0.007 ( stat ) ± 0.008 ( syst ) .