Van der Waals (vdW) heterostructures of two-dimensional monolayers are a relatively new class of materials with highly tunable band alignment, bandgap energy, and bandgap transition type. In this study, we performed density functional theory calculations to investigate how a vdW heterostructure of heptazine-based graphitic carbon nitride (hg-C3N4) and graphitic zinc oxide (g-ZnO) monolayers is formed (hg-C3N4/g-ZnO). This heterostructure is a potential solar-driven photocatalyst for the water-splitting reaction. Upon the formation of the heterostructure, a type-I indirect bandgap (Eg = 2.08 eV) is created with appropriate conduction band minimum and valence band maximum levels relative to the oxidation/reduction potentials for the water-splitting reaction. In addition, a very large electrostatic potential difference of 11.18 eV is generated across the heterostructure, leading to a large, naturally-formed, built-in electric field directing from hg-C3N4 to g-ZnO. The produced electric field forces photogenerated electrons in g-ZnO to transfer toward hg-C3N4, leading to a decrease in the electron-hole recombination rate. We also found that both g-ZnO and hg-C3N4 synergistically lead to higher light absorption of the heterostructure (λmax = 387 nm). Furthermore, band alignment, bandgap energy, and transition type of the heterostructure can be tuned by applying external perpendicular electric fields and biaxial strains. It was found that a strain of +2% leads to a Z-scheme band alignment (Eg = 2.34 eV, direct) and an electric field of 1 V Å-1 leads to a type-II heterostructure (Eg = 2.29 eV, indirect), which are both beneficial for efficient water-splitting photocatalysis.