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Effects of intrinsic spin-orbit coupling in MoS2 nanotubes are studied for the first time. To this end, the double group formalism is applied, yielding model-independent information on band/spin splitting and possible spin orientation. Next, full symmetry-based density functional tight-binding calculations are performed in order to gain detailed insight into the curvature impact on the magnitude of the allowed spin-orbit effects. Large splitting in the vicinity of point occurs regardless of tube chirality. On the other hand, at the position of the direct gap in armchair tubes, band splitting of the valence bands is smaller than the splitting reported in the monolayer. Thus, in contrast to the carbon analogues, in MoS2 nanotubes, the curvature may decrease or increase the splitting. To enlighten these effects, detailed orbital contribution of atomic orbitals is studied. Copyright © 2020 American Chemical Society.