Paralytic shellfish poisoning (PSP) is a human foodborne syndrome caused by the consumption of shellfish that accumulate paralytic shellfish toxins (PSTs, saxitoxin group). In PST-producing dinoflagellates such as Alexandrium spp., toxin synthesis is encoded in the nuclear genome via a gene cluster (sxt). Toxin production is supposedly associated with the presence of a 4th domain in the sxtA gene (sxtA4), one of the core genes of the PST gene cluster. It is postulated that gene expression in dinoflagellates is partially constitutive, with both transcriptional and post-transcriptional processes potentially co-occurring. Therefore, gene structure and expression mode are two important features to explore in order to fully understand toxin production processes in dinoflagellates. In this study, we determined the intracellular toxin contents of twenty European Alexandrium minutum and Alexandrium pacificum strains that we compared with their genome size and sxtA4 gene copy numbers. We observed a significant correlation between the sxtA4 gene copy number and toxin content, as well as a moderate positive correlation between the sxtA4 gene copy number and genome size. The 18 toxic strains had several sxtA4 gene copies (9–187), whereas only one copy was found in the two observed non-toxin producing strains. Exploration of allelic frequencies and expression of sxtA4 mRNA in 11 A. minutum strains showed both a differential expression and specific allelic forms in the non-toxic strains compared with the toxic ones. Also, the toxic strains exhibited a polymorphic sxtA4 mRNA sequence between strains and between gene copies within strains. Finally, our study supported the hypothesis of a genetic determinism of toxin synthesis (i.e., the existence of several genetic isoforms of the sxtA4 gene and their copy numbers), and was also consistent with the hypothesis that constitutive gene expression and moderation by transcriptional and post-transcriptional regulation mechanisms are the cause of the observed variability in the production of toxins by A. minutum.