Correlated electrons in transition metal oxides exhibit a variety of emergent phases. When transition metal oxides are confined to a single-atomic-layer thickness, experiments so far have shown that they usually lose diverse properties and become insulators. In an attempt to extend the range of electronic phases of the single-atomic-layer oxide, we search for a metallic phase in a monolayer-thick epitaxial SrRuO3 film. Combining atomic-scale epitaxy and angle-resolved photoemission measurements, we show that the monolayer SrRuO3 is a strongly correlated metal. Systematic investigation reveals that the interplay between dimensionality and electronic correlation makes the monolayer SrRuO3 an incoherent metal with orbital-selective correlation. Furthermore, the unique electronic phase of the monolayer SrRuO3 is found to be highly tunable, as charge modulation demonstrates an incoherent-to-coherent crossover of the two-dimensional metal. Our work emphasizes the potentially rich phases of single-atomic-layer oxides and provides a guide to the manipulation of their two-dimensional correlated electron systems.