In search of new probes for biomolecules, the spectral fluorescent study of four monomethine cyanine dyes (MCD), both unsymmetrical and symmetrical, has been carried out in different organic solvents, in aqueous buffer solutions, and in the presence of DNA and HSA. The complexation of MCD with biomacromolecules leads to a steep growth of the fluorescence intensity. Complexes of MCD with dsDNA and HSA of various types were modeled in silico by molecular docking. Experiments on thermal dissociation of dsDNA in the presence of MCD showed the formation of intercalative complexes of MCD with DNA. Quenching of intrinsic fluorescence of HSA by MCD occurred with rate constants much higher than the diffusion limit, that is, in dye–HSA complexes. Effective constants of MCD complexation with the biomacromolecules were estimated. MCD 1 has the best characteristics as a possible fluorescent probe for dsDNA and can serve as a sensitive and selective probe for dsDNA in the presence of HSA. Photochemical properties of MCD complexed with DNA have been also studied. An increase in the quantum yield of the triplet states of MCD in complexes with DNA has been found, which may be important for using these dyes as potential candidates in photodynamic therapy.