Tyrosine (Tyr) is involved in the synthesis of neurotransmitters, catecholamines, thyroid hormones, etc. Multiple pathologies are associated with impaired Tyr metabolism. Silver nanoclusters (Ag NCs) can be applied for colorimetric, fluorescent, and surface-enhanced Raman spectroscopy (SERS) detection of Tyr. However, one should understand the theoretical basics of interactions between Tyr and Ag NCs. Thereby, we calculated the binding energy (Eb) between Tyr and Agnq (n = 1–8; q = 0–2) NCs using the density functional theory (DFT) to find the most stable complexes. Since Ag NCs are synthesized on Tyr in an aqueous solution at pH 12.5, we studied Tyr−1, semiquinone (SemiQ−1), and Tyr−2. Ag32+ and Ag5+ had the highest Eb. The absorption spectrum of Tyr−2 significantly red-shifts with the attachment of Ag32+, which is prospective for colorimetric Tyr detection. Ag32+ interacts with all functional groups of SemiQ−1 (phenolate, amino group, and carboxylate), which makes detection of Tyr possible due to band emergence at 1324 cm−1 in the vibrational spectrum. The ground state charge transfer between Ag and carboxylate determines the band emergence at 1661 cm−1 in the Raman spectrum of the SemiQ−1–Ag32+ complex. Thus, the prospects of Tyr detection using silver nanoclusters were demonstrated.