A two-dimensional (2D) MA₂Z₄ family with and phases has been attracting tremendous interest, the MoSi₂N₄ and WSi₂N₄ of which have been successfully fabricated ( Science 369, 670 (2020)). Janus monolayers have been achieved in many 2D families, so it is interesting to construct a Janus monolayer from the MA₂Z₄ family. In this work, Janus MSiGeN₄ (M = Zr and Hf) monolayers are predicted from -MA₂Z₄, which exhibit dynamic, mechanical and thermal stabilities. It is found that they are indirect band-gap semiconductors by using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). With biaxial strain from 0.90 to 1.10, the energy band gap shows a nonmonotonic behavior due to a change of conduction band minimum (CBM). A semiconductor to metal transition can be induced by both compressive and tensile strains, and the phase transformation point is about 0.96 for compressive strain and 1.10 for tensile strain. The tensile strain can change the positions of CBM and valence band maximum (VBM), and can also induce the weak Rashba-type spin splitting near CBM. For MSiGeN₄ (M = Zr and Hf) monolayers, both an in-plane and out-of-plane piezoelectric response can be produced, when a uniaxial strain in the basal plane is applied, which reveals the potential as piezoelectric 2D materials. The high absorption coefficients in the visible light region suggest that MSiGeN₄ (M = Zr and Hf) monolayers have potential photocatalytic applications. Our works provide an idea to achieve a Janus structure from the MA₂Z₄ family, and can hopefully inspire further research exploring Janus MA₂Z₄ monolayers.