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Modulation of electronic properties of materials by electric fields provides access to complex electronic behaviors and greater freedom in tuning the energy bands of materials. Here, we explore one-dimensional (1D) superlattices induced by a confining electrostatic potential in monolayer MoS₂, a prototypical two-dimensional semiconductor. [1] Using density functional theory calculations, we show that 1D periodic potentials applied to monolayer MoS₂ induce electrostatic superlattices in which the response is dominated by structural distortions relative to purely electronic effects. These structural distortions reduce the intrinsic band gap of the monolayer substantially while also polarizing the monolayer through piezoelectric coupling, resulting in spatial separation of charge carriers as well as Stark shifts that produce dispersive minibands. Importantly, these minibands inherit the valley-selective magnetic properties of monolayer MoS₂, enabling fine control over spin-valley coupling in MoS₂ and similar transition-metal dichalcogenides.