Considering our previous findings on the remarkable activity exhibited by cobalt(III) with 2-acetylpyridine-N(4)-R-thiosemicarbazone (Hatc-R) compounds against Mycobacterium tuberculosis, the present study aimed to explored new structure features of the complexes of the type [Co(atc--R)2]Cl, where R = methyl (Me, 1) or phenyl (Ph, 2) (13C NMR, high-resolution mass spectrometry, LC–MS/MS, fragmentation study) together with its antibacterial and antiviral biological activities. The minimal inhibitory and minimal bactericidal concentrations (MIC and MBC) were determined, as well as the antiviral potential of the complexes on chikungunya virus (CHIKV) infection in vitro and cell viability. [Co(atc-Ph)2]Cl revealed promising MIC and MBC values which ranged from 0.39 to 0.78 µg/mL in two strains tested and presented high potential against CHIKV by reducing viral replication by up to 80%. The results showed that the biological activity is strongly influenced by the peripheral substituent groups at the N(4) position of the atc-R1− ligands. In addition, molecular docking analysis was performed. The relative binding energy of the docked compound with five bacteria strains was found in the range of −3.45 and −9.55 kcal/mol. Thus, this work highlights the good potential of cobalt(III) complexes and provide support for future studies on this molecule aiming at its antibacterial and antiviral therapeutic application.