The magnetization of a quantum magnet can be pinned at a fraction of its saturated value by collective effects. One example of such a plateau phase is found in spin-1/2 triangular-lattice antiferromagnets. They feature strong geometrical frustration and the plateau phase therein is often interpreted as arising from an order-by-disorder mechanism driven by quantum fluctuations. Here we observe a one-third magnetization plateau under an applied magnetic field in the spin-1 antiferromagnet Na3Ni2BiO6 with a honeycomb lattice, which, with conventional magnetic interactions, would not be geometrically frustrated. Based on our elastic neutron scattering measurements, we propose the spin structure of the plateau phase to be an unusual partial spin-flop ferrimagnetic order. Our theoretical calculations indicate that bond-anisotropic Kitaev interactions are the source of frustration that produces the plateau. These results suggest that Kitaev interactions provide a different route to frustration and phases driven by quantum fluctuations in high-spin magnets.