There is a broad consensus that individual differences in working memory capacity (WMC) are strongly related to individual differences in intelligence. However, correlational studies do not allow conclusions about the causal nature of the relationship between WMC and fluid intelligence. While research on the cognitive basis of intelligence typically assumes that simpler lower-level cognitive processes contribute to individual differences in higher-order reasoning processes, a reversed causality or a third variable giving rise to two intrinsically uncorrelated variables may exist. In the present study, we investigated the causal nature of the relationship between WMC and intelligence by assessing the experimental effect of working memory load on intelligence test performance. Moreover, we tested if the effect of working memory load on intelligence test performance increased under time constraints, as previous studies have shown that the association between the two constructs increases if intelligence tests are administered with a strict time limit. We show in a sample of 65 participants that working memory load impaired intelligence test performance, but that this experimental effect was not affected by time constraints, which suggests that the experimental manipulations of working memory capacity and processing time did not affect the same underlying cognitive process. Our results confirm that WMC causally contributes to higher-order reasoning processes. Remarkably, we found that the introduction of time constraints completely nullified the advantage of more intelligent participants in matrix reasoning test performance, which emphasizes the role of processing speed as an elementary cognitive process parameter underlying individual differences in intelligence.