Skilled tool use and object manipulation critically relies on the ability to scale anticipatorily the grip force (GF) in relation to object dynamics. This predictive behaviour entails that the nervous system is able to store, and then select, the appropriate internal representation of common object dynamics, allowing GF to be applied in parallel with the arm motor commands. Although psychophysical studies have provided strong evidence supporting the existence of internal representations of object dynamics, known as "internal models", their neural correlates are still debated. Because functional neuroimaging studies have repeatedly designated the supplementary motor area (SMA) as a possible candidate involved in internal model implementation, we used repetitive transcranial magnetic stimulation (rTMS) to interfere with the normal functioning of left or right SMA in healthy participants performing a grip-lift task with either hand. TMS applied over the left, but not right, SMA yielded an increase in both GF and GF rate, irrespective of the hand used to perform the task, and only when TMS was delivered 130-180 ms before the fingers contacted the object. We also found that both left and right SMA rTMS led to a decrease in preload phase durations for contralateral hand movements. The present study suggests that left SMA is a crucial node in the network processing the internal representation of object dynamics although further experiments are required to rule out that TMS does not affect the GF gain. The present finding also further substantiates the left hemisphere dominance in scaling GF.