Moire superlattices of two-dimensional van der Waals materials have emerged as a powerful platform for designing electronic band structures and discovering emergent physical phenomena. A key concept involves the creation of long-wavelength periodic potential and moire bands in a crystal through interlayer hybridization when two materials are overlaid. Here we demonstrate a new approach based on spatially periodic dielectric screening to create moire bands in a monolayer semiconductor. It relies on reduced dielectric screening of the Coulomb interactions in monolayer semiconductors and their environmental dielectric-dependent electronic band structure. We observe optical transitions between moire bands in monolayer WSe$_{2}$ when it is placed close to small angle-misaligned graphene on hexagonal boron nitride. The moire bands are a result of long-range Coulomb interactions, strongly gate-tunable, and can have versatile superlattice symmetries independent of the crystal lattice of the host material. Our result also demonstrates that monolayer semiconductors are sensitive local dielectric sensors.