The literature reports that the supplementary motor area (SMA) and pre-supplementary motor area (pre-SMA) are involved in motor planning and execution, and in motor-related cognitive functions such as motor imagery. However, their specific role in action language processing remains unclear. In the present study, we investigated the impact of repetitive transcranial magnetic stimulation (rTMS) over SMA and pre-SMA during an action semantic analogy task (SAT) in relation with fine motor skills (i.e., manual dexterity) and motor imagery abilities in healthy non-expert adults. The impact of rTMS over SMA (but not pre-SMA) on reaction times (RT) during SAT was correlated with manual dexterity. Specifically, results show that rTMS over SMA modulated RT for those with lower dexterity skills. Our results therefore demonstrate a causal involvement of SMA in action language processing, as well as the existence of inter-individual differences in this involvement. We discuss these findings in light of neurolinguistic theories of language processing.