Solution processed colloidal quantum dot (CQD) solar cells have great potential for large area low-cost photovoltaics. However, light utilization remains low mainly due to the tradeoff between small carrier transport lengths and longer infrared photon absorption lengths. Here, we demonstrate a bottom-illuminated periodic nanostructured CQD solar cell that enhances broadband absorption without compromising charge extraction efficiency of the device. We use finite difference time domain (FDTD) simulations to study the nanostructure for implementation in a realistic device and then build proof-of-concept nanostructured solar cells, which exhibit a broadband absorption enhancement over the wavelength range of λ = 600 to 1,100 nm, leading to a 31% improvement in overall short-circuit current density compared to a planar device containing an approximately equal volume of active material. Remarkably, the improved current density is achieved using a light-absorber volume less than half that typically used in the best planar devices.