Changes in the concentration of free amino acids in biological tissues is a sign of impaired protein metabolism in patients with cancer. Recently, Raman spectroscopy has been used for early diagnostics of oncological diseases. The concentrations of individual components of biological tissue (for instance, the concentrations of amino acids) can be obtained by decomposing the tissue Raman spectrum. This study was designed to evaluate the effect of noise in the Raman spectra of individual amino acids on the result of the decomposition of the spectra of an amino acid mixture. As a decomposition method, we used Multivariate Curve Resolution-Alternating Least Squares (MCR–ALS) analysis and investigate experimental Raman spectra of amino acids and mathematically simulated Raman spectra of amino acid mixtures. Noise with different signal-to-noise ratios (SNR) was artificially added to both the experimental spectra of pure amino acids and the spectra of the mixtures. Concentration values for each amino acid obtained as a result of applying the MCR–ALS analysis have been compared with the corresponding true values and the correlation coefficients have been calculated. The results show a less pronounced negative effect of noise in the case when the spectra of pure amino acids (which were used as a basis for the MCR–ALS analysis) are noisy, and a more pronounced negative effect when the spectrum of the mixture is noisy. The accuracy of reconstruction of an amino acid is also negatively affected by strong background fluorescence in the amino acid spectrum. Moreover, the results indicate that using the basis spectra with a high SNR (SNR = 5) makes it possible to successfully estimate the amino acid concentrations in a mixture even when the Raman spectrum of the mixture is noisy and has a low SNR (SNR < 5).