In the realm of two-dimensional materials, magnetic and transport properties of a unique representative ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ attract ever increasing attention. Here, we use a developed first-principles method for calculating laser-induced response to study the emergence of photoinduced currents of charge and spin in single-layer ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$, which are of second order in the electric field. We provide a symmetry analysis of the emergent photocurrents in the system, finding it to be in excellent agreement with ab initio calculations. We analyze the magnitude and behavior of the charge photocurrents with respect to disorder strength, frequency, and band filling. Remarkably, not only do we find a large charge current response, but also predict that ${\mathrm{Fe}}_{3}{\mathrm{GeTe}}_{2}$ can serve as a source of significant laser-induced spin currents, which makes this material as a promising platform for various applications in optospintronics.