Data corresponds to the demonstration of the first memtransistor on monolayer MoS2. Polycrystalline monolayer MoS2 was grown by chemical vapor deposition with grain sizes of 3-5 microns. Memtransistor devices were fabricated on Si substrates coated with 300 nm thermal oxide by following custom-made photolithography and reactive ion etching recipes. Characterization of the devices using atomic force microscopy, electrostatic force microscopy, and cryogenic measurement revealed switching mechanism governed by a dynamically tunable Schottky barrier at contact. Schottky barrier tuning, as modeled by a device physics model, arises from the migration of defects near metal edge possibly assisted by grain boundaries. The devices show large resistive switching ratios, large gate-tunability of resistive switching ratio, retention of distinct states for at least 24 hours, the endurance of >400 cycles, and some device to device variability. The device is compatible with multi-terminal architecture thus mimicking biological neurons.