The majority of dry pet food currently on the market is produced using fresh meats (FMs) and especially meat meals (MMs) as the main protein source. The transport and storage conditions of the raw materials, together with thermal and mechanical treatments in the case of MMs, may result in undesirable alterations of food products and their protein content. This study was conducted to analyze the protein component of three different kinds of raw materials used for dry pet food production, i.e., chicken, pork, and salmon. The quantitative analysis of the protein component was determined using the traditional Kjeldahl method and near-infrared (NIR) spectroscopy, and an alternative method, i.e., the Bradford assay, while the qualitative analysis was performed through SDS-PAGE, followed by Coomassie Blue staining. The amino acid (AA) profile was also evaluated by quadrupole time-of-flight liquid chromatography/mass spectrometry (Q-TOF LC/MS). In addition, the digestibility was tested through in vitro gastric and small intestine digestion simulation. Statistical analysis was performed by the Student’s t-test, and data are reported as mean ± SEM, n = 10 (p < 0.05). The results showed that the MMs are lower in quality compared to FMs, both in terms of protein bioavailability and digestibility, having a lower soluble protein (SP) content (chicken MM = 8.6 g SP/100 g dry sample; pork MM = 6.2 g SP/100 g dry sample; salmon MM = 7.9 g SP/100 g dry sample) compared to FMs (chicken FM = 14.6 g SP/100 g dry sample; pork FM = 15.1 g SP/100 g dry sample; salmon FM = 13.7 g SP/100 g dry sample). FMs appear, therefore, to be higher-quality ingredients for pet food production. Moreover, the Bradford assay proved to be a quick and simple method to better estimate protein bioavailability in the raw materials used for dry pet food production, thanks to its correlation with the in vitro digestibility.