The Indus Canyon in the northwestern Indian Ocean has been reported to be the site of numerous submarine mass failures in the past. This study is the first to investigate potential tsunami hazards associated with such mass failures in this region. We employed statistical emulation, i.e. surrogate modelling, to efficiently quantify uncertainties associated with slump-generated tsunamis at the slopes of the canyon. We simulated 60 slump scenarios with thickness of 100-300 m, width of 6-10.5 km, travel distances of 500-2000 m and submergence depth of 250-450 m. These scenarios were then used to train the emulator and predict 500,000 trial scenarios in order to study probabilistically the tsunami hazard over the near field. Due to narrow-deep canyon walls and the shallow continental shelf in the adjacent regions (\100 m water depth), the tsunami propagation has a unique pattern as an ellipse stretched in the NE-SW direction. The results show that the most likely tsunami amplitudes and velocities are approximately 0.2-1.0 m and 2.5-13 m/s, respectively, which can potentially impact vessels and maritime facilities. We demonstrate that the emulator-based approach is an important tool for probabilistic hazard analysis since it can generate thousands of tsunami scenarios in few seconds, compared to days of computations on High Performance Computing facilities for a single run of the dispersive tsunami solver that we use here.