Superconductors can form ideal diodes carrying nondissipative supercurrents in the forward direction and dissipative currents in the backward direction. The Josephson diode has proven to be a promising design where the junction between the two superconductors comprises the weakest link and thus provides the dominant mechanism. We here propose a Josephson diode based on a single magnetic material with a conical spin structure. The helical spin rotation produces Rashba-like band splitting inversely proportional to the rotation period. Together with the Zeeman splitting caused by the time-reversal symmetry breaking of the noncoplanar spin texture, this results in a large diode efficiency close to the transition of the magnetic Josephson junction.