The type and quantity of precursor amino acids present in grape must that are used by wine yeasts affect the organoleptic and health properties of wine. The aim of this work was to conduct a preliminary screening among Saccharomyces and non-Saccharomyces indigenous strains, which were previously isolated from different Italian regional grape varieties. This was performed in order to evaluate their decarboxylase activity on certain important amino acids—such as arginine, proline, serine, and tyrosine—that are present in grape must. In particular, a qualitative test on 122 wine yeasts was performed on a decarboxylase medium using arginine, proline, serine, and tyrosine as precursor amino acids. Our results showed a considerable variability among the microbial species tested for this parameter. Indeed, Saccharomyces cerevisiae strains exhibited a high decarboxylase capability of the four amino acids tested; moreover, only 10% of the total (i.e., a total of 81) did not show this trait. A high recovery of decarboxylation ability for at least one amino acid was also found for Zygosaccharomyces bailii and Hanseniaspora spp. These findings can, therefore, promote the inclusion of decarboxylase activity as an additional characteristic in a wine yeast selection program in order to choose starter cultures that possess desirable technological traits; moreover, this also can contribute to the safeguarding of consumer health.