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Photoinduced phase transitions are attracting intensive interest recently. Many theoretical studies have been conducted using the Floquet theory since pioneering work by Oka and Aoki which theoretically predicted the photoinduced topological phase transition in graphene. However, for further development of this growing field, proposals of novel target materials and predictions of interesting physical phenomena from theoretical side are eagerly anticipated. Under these circumstances, we theoretically predicted the occurrence of photoinduced topological phase transition in the organic salt α-(BEDT-TTF)₂I₃ under irradiation with circularly polarized light. By analyzing band structures, Chern numbers, and Hall conductivity in a photoirradiated system, we obtain a rich nonequilibrium phase diagram in plane of the amplitude and frequency of light, which includes Chern insulator, non-topological insulator, and semimetal phases. In addition, calculations of the Hall conductivity using the Floquet-Keldysh formalism predicted that the quantization of Hall conductivity can be observed also in this photoinduced Chern insulator phase. These results widen a range of target materials and contribute to the development of research for the optical manipulation of electronic states in matters.