Individuals with high working memory capacity (WMC) are less distracted by task-irrelevant speech than others. The mechanism behind this relationship, however, is not well understood, and it has only been found in a few paradigms. We used a Number updating task to measure WMC and two suppression mechanisms (immediate and delayed), and tested how they were associated with individual differences in susceptibility to the effects of speech on reading comprehension. The results revealed a negative relationship between WMC and susceptibility to speech distraction. Of the two suppression mechanisms, only immediate suppression was associated with speech distraction, suggesting that susceptibility to distraction is determined by the ability to immediately suppress the irrelevant speech. Furthermore, the relationship between WMC and speech distraction was mediated by the immediate suppression mechanism. The implications of these results and possible explanations of similar results found in other paradigms are discussed.