In this study, the magnetic ground state of iridium perovskites (Srn+1IrnO3n+1, where n = 1, 2, and ∞) was considered using muon spin spectroscopy (µSR). When probed by muons in Sr2IrO4 and Sr3Ir2O7 (n = 1, 2), the internal field (B loc ) showed clear sign of a magnetic order in two stages at transition temperatures TN ≃ 230 K and Tm ≃ 90 K in Sr2IrO4 and TN ≃ 280 K and Tm ≃ 70 K in Sr3Ir2O7, respectively. In contrast, no long-range magnetic order was observed in orthorhombic SrIrO3 (n = ∞). Based on the known magnetic structure in Sr2IrO4 and Sr3Ir2O7, we successfully identified muon sites in these compounds from the magnitude of B loc in the first stage (Tm ≤ T ≤ TN). Below Tm, B loc probed by a fraction of muons occupying sites near the apical oxygen of IrO6 octahedra exhibited a further increase but remained mostly unchanged for sites close to the in-plane oxygen. While such behavior cannot be explained by the alteration of the Ir spin structure, it is consistent with the selective appearance of ordered magnetic moments on the apical oxygen. The oxygen polarization was also in line with the reported magnetization anomalies in these compounds below ∼ Tm. A possible link between the oxygen polarization and ferroelectric (multiferroic) behavior in Sr2IrO4 was considered.