We explore a new mechanism for switching magnetism and superconductivity in a magnetically frustrated iron-based superconductor using spin-polarized scanning tunneling microscopy (SPSTM). Our SPSTM study on single-crystal Sr_{2}VO_{3}FeAs shows that a spin-polarized tunneling current can switch the Fe-layer magnetism into a nontrivial C_{4} (2×2) order, which cannot be achieved by thermal excitation with an unpolarized current. Our tunneling spectroscopy study shows that the induced C_{4} (2×2) order has characteristics of plaquette antiferromagnetic order in the Fe layer and strongly suppresses superconductivity. Also, thermal agitation beyond the bulk Fe spin ordering temperature erases the C_{4} state. These results suggest a new possibility of switching local superconductivity by changing the symmetry of magnetic order with spin-polarized and unpolarized tunneling currents in iron-based superconductors.