[en] The single-spin asymmetry A_N in the reaction π^- + d_↑^→ π⁰ + X in the beam-fragmentation region at the energy of 40 GeV was investigated by using the PROZA setup installed at the U-70 accelerator of the Institute for High Energy Physics (IHEP, Protvino). It was measured to be A_N = (13.6 ± 2.6(stat.) ± 2.0(syst.))% in the intervals 0.7 < x_F < 1.0 and 1.0 < p_T < 1.8 GeV/c. The results agree with the asymmetry of π⁰ mesons in the charge-exchange reaction π^- + p_↑^→ π⁰ + n at the same values of the transverse momentum and beam energy. The asymmetry in the reaction K^- + d_↑^→ π⁰ + X was simultaneously measured and found to be A_N = (11 ± 14)% for p_T > 1.2 GeV/c.