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A new hydrogen-bonded charge-transfer (HB-CT) complex formed between the donor 2-amino-4-methoxy-6-methylpyrimidine (AMMP) and the π-acceptor 2,5-dihydroxy-p-benzoquinone (DHBQ) was investigated in both solid and solution states. The investigation was conducted using UV-Vis, CHN, FTIR, 1H NMR, XRD, and TG-DTA analyses. The molecular composition of the CT complex in MeOH was found to be 1 : 1. The formation constant (KCT), molecular extinction coefficient (ε), and several other spectroscopic physical parameters were evaluated at different temperatures. The thermodynamic properties of the CT interaction in MeOH were studied by calculating the enthalpy (ΔH°), entropy (ΔS°), and free energy (ΔG°). The thermodynamic parameters indicated that van der Waals interactions and hydrogen bonding occur between AMMP and DHBQ in MeOH. The CHN, FTIR, and TG-DTA measurements confirmed that the solid HB-CT complex forms in a 2 : 1 ratio, i.e., [(AMMP)2(DHBQ)], and exhibits high stability. Moreover, XRD analysis was used to establish that the mean particle size of the complex is 23 nm. Finally, the solid HB-CT complex was screened for its antibacterial, antifungal, and antioxidant activities. It shows good activity against various bacterial and fungal species. Furthermore, the HB-CT complex exhibits good DPPH scavenging activity.