The aim of this study was to analyse the associations between the consumption of different types of meat and the muscle strength index (MSI) and to examine whether this relationship is mediated by total protein intake (TPI) and lean mass percentage (LM%) in young adults. We conducted a cross-sectional study with first-year university students from Castilla-La Mancha, Spain. Different types of meat consumption (total, red, processed, and white and fish) were separately evaluated using a Food-Frequency Questionnaire. MSI was determined from the handgrip and standing long jump tests. ANCOVA models were used to test the mean differences in MSI by categories of meat consumption. Serial multiple mediation models were used to explore the mediating role of TPI and LM% in the relationship between meat consumption and MSI. All analyses were adjusted for age, sex, and socioeconomic level, identified through a directed acyclic graph. Additional analyses were performed with a small subsample including alcohol intake, tobacco smoking, physical activity, cardiorespiratory fitness, and total energy intake as covariates in the multiple mediation models. A total of 230 students (mean age 21.1 ± 2.1years, 66.5% women) were included in the analysis. Young adults with higher meat consumption (total, red, and white and fish) had higher MSI adjusted means than their peers with lower meat consumption (p < 0.05). These associations did not remain after controlling for TPI and LM%. In adjusted mediation analyses, a significant indirect effect was observed through TPI and LM% in the associations between each of the types of meat consumption and MSI. In the additional analyses, a greater effect of white and fish meat consumption on muscle strength through mediation of TPI and LM% was reported compared to red or processed meat consumption, and no significant effects were observed between processed meat consumption and MSI. Higher consumption of total, red, and white and fish meat was associated with increased MSI in young adults. TPI and LM% mediated this relationship.