At present, the research on two-dimensional (2D) ferromagnets is mainly concentrated on van der Waals materials, while the successful preparation of strain-free freestanding 2D perovskite films provides a great opportunity for designing 2D ferromagnets beyond van der Waals materials. Perovskite oxide SrRuO₃, a typical perovskite itinerant ferromagnet, has broad application prospects in many fields. In this work, the lattice dynamics, ground-state structure, electronic and magnetic properties of its perovskite monolayer with formula Sr₂RuO₄, as well as the effect of external electric field, are studied by combining first-principles calculation, symmetry analysis and Monte Carlo simulation. The influence of the Hubbard parameter U is also revealed. The results indicate that the ground-state structure under all U values presents the structural phase (space group P4/mbm) generated by octahedral rotation distortion. Similar to the SrRuO₃ bulk, Sr₂RuO₄ has a monolayer ground-state phase that exhibits ferromagnetism, which is independent of the U value and thus robust. Density functional theory calculation using Hubbard parameter U predicts the ground-state phase of the monolayer to be a ferromagnetic half metal with an out-of-plane easy-magnetization axis, while excluding that the U parameter predicts the ground-state phase to be a ferromagnetic metallic state. The ferromagnetism mainly originates from the strong ferromagnetic exchange interaction between the nearest neighbor spin pairs. The simulated Curie temperature of the Sr₂RuO₄ monolayer is 177 K, which is close to the value (150 K) of its bulk phase. The out-of-plane electric field does not change the ground-state structure nor ferromagnetism of the Sr₂RuO₄ monolayer, but can significantly modulate its electronic property and magnetic property. When an external electric field exceeding 0.3 V/Å is applied, the system undergoes a transition from a ferromagnetic half-metal state to a ferromagnetic metallic state. This work indicates the potential application of Sr₂RuO₄ monolayer in low-dimensional spintrnic devices, and provides a reference for developing perovskite-based 2D ferromagnets and realizing the control of 2D magnetism by electric field.