Nonlinear optical responses to external electromagnetic field, characterized by second- and higher-order susceptibilities, play crucial roles in nonlinear optics and optoelectronics. Here, we demonstrate the possibility to achieve ferroicity-driven nonlinear photocurrent switching in time-reversal invariant multiferroics. It is enabled by the second-order current response to electromagnetic field whose direction can be controlled by both internal ferroic orders and external light polarization. Second-order direct photocurrent consists of shift current and circular photocurrent under linearly and circularly polarized light irradiation, respectively. We elucidate the microscopic mechanism in a representative class of two-dimensional multiferroic materials using group theoretical analyses and first-principles theory. The complex interplay of symmetries, shift vector, and Berry curvature governs the fundamental properties and switching behavior of shift current and circular photocurrent. Ferroicity-driven nonlinear photocurrent switching will open avenues for realizing nonlinear optoelectronics, nonlinear multiferroics, etc., using the coupled ferroic orders and nonlinear responses of ferroic materials under external field.