Pyrochlore iridates A2Ir2O7 (A = rare earth elements, Y or Bi) hold great promise for realizing novel electronic and magnetic states owing to the interplay of spin-orbit coupling, electron correlation, and geometrical frustration. A prominent example is the formation of all-in/all-out (AIAO) antiferromagnetic order in the Ir4 + sublattice that comprises corner-sharing tetrahedra. Here we report on an unusual magnetic phenomenon, namely, a cooling-field-induced shift of magnetic hysteresis loop along the magnetization axis, and its possible origin in pyrochlore iridates with nonmagnetic Ir defects (e.g., Ir3 +). In a simple model, we attribute the magnetic hysteresis loop to the formation of ferromagnetic (FM) droplets in the AIAO antiferromagnetic (AFM) background. The weak ferromagnetism originates from canted antiferromagnetic order of the Ir4 + moments surrounding each nonmagnetic Ir defect. The shift of hysteresis loop can be understood quantitatively based on an exchange-bias-like effect in which the moments at the shell of the FM droplets are pinned by the AIAO AFM background via mainly the Heisenberg (J ) and Dzyaloshinsky-Moriya (D ) interactions. The magnetic pinning is stable and robust against sweeping cycle and sweeping field up to 35 T, which is possibly related to the magnetic octupolar nature of the AIAO order.