MoS2 nanoscrolls that have inner core radii of similar to 250 nm are generated from MoS2 monolayers, and the optical and transport band gaps of the nanoscrolls are investigated. Photoluminescence spectroscopy reveals that a MoS2 monolayer, originally a direct gap semiconductor (similar to 1.85 eV (optical)), changes into an indirect gap semiconductor (similar to 1.6 eV) upon scrolling. The size of the indirect gap for the MoS2 nanoscroll is larger than that of a MoS2 bilayer (similar to 1.54 eV), implying a weaker interlayer interaction between concentric layers of the MoS2 nanoscroll compared to Bernal-stacked MoS2 few-layers. Transport measurements on MoS2 nanoscrolls incorporated into ambipolar ionic-liquid-gated transistors yielded a band gap of similar to 1.9 eV. The difference between the transport and optical gaps indicates an exciton binding energy of 0.3 eV for the MoS2 nanoscrolls. The rolling up of 2D atomic layers into nanoscrolls introduces a new type of quasi-1D nanostructure and provides another way to modify the band gap of 2D materials.