Although the kagome model is fundamentally two-dimensional, the essential kagome physics, i.e., the kagome-bands-driven emergent electronic states, has yet to be explored in the monolayer limit. Here, we present the experimental realization of kagome physics in monolayer Mo33Te56, showcasing both ferromagnetic ordering and a correlated insulating state with an energy gap of up to 15 meV. Using a combination of scanning tunnelling microscopy and theoretical calculations, we find a structural phase of the monolayer Mo-Te compound, which forms a mirror-twin boundary loop superlattice exhibiting kagome geometry and multiple sets of kagome bands. The partial occupancy of these nearly flat bands results in Fermi surface instability, counteracted by the emergence of ferromagnetic order (with a coercive field ~0.1 T, as observed by spin-polarized STM) and the opening of a correlated hard gap. Our work establishes a robust framework featuring well-defined atomic and band structures, alongside the intrinsic two-dimensional nature, essential for the rigorous examination of kagome physics.