Aptamers offer several advantages over antibodies. However, to ensure high affinity and specificity, a better understanding of the interactions between the nucleic-acid-based aptamers and their targets is mandatory. Therefore, we investigated the influence of two physical properties of proteins—molecular mass and charge—on the affinity of nucleic-acid-based aptamers. For this purpose, first, the affinity of two random oligonucleotides towards twelve proteins was determined. No binding was observed for proteins with a negative net charge towards the two oligonucleotides, while up to nanomolar affinity was determined for positively charged proteins with a high pI value. Second, a literature analysis comprising 369 aptamer–peptide/protein pairs was performed. The dataset included 296 different target peptides and proteins and is thus currently one of the largest databases for aptamers for proteins and peptides. The targets considered covered isoelectric points of 4.1–11.8 and a molecular weight range of 0.7–330 kDa, while the dissociation constants ranged from 50 fM to 29.5 µM. This also revealed a significant inverse correlation between the protein’s isoelectric point and the affinity of aptamers. In contrast, no trend was observed between the affinity and the molecular weight of the target protein with either approach.