The effect of copper substitution by alkali metals on the properties of chalcopyrite-type materials for tandem applications in photovoltaics is investigated at the first-principles level, using an exchange-correlation hybrid functional optimized to yield a description of the structural, electronic, and dynamic properties of these materials in good agreement with experiment. Since the target values of the band gap for tandem applications should be between 1.5 and 1.8 eV, one part of the results concerned the variation of calculated band gap values under the effect of substitution. A systematic study of the effects of Li, Na, K, Rb, and Cs on the structural, electronic, and thermodynamic properties of CuGaS2, CuGaSe2, CuInS2, and CuInSe2 has been performed. The evolution of the crystallographic cell with the concentration of alkali metals turned out to be of two types: (i) the substitution of Cu with Li and Na in CuInS2, irrespective of concentration, leaves the underlying chalcopyrite structure unchanged, affecting only the lattice parameters; (ii) the substitution of Cu with Na (with the exception of CuInS2), K, Rb, and Cs at sufficiently high concentration brings about a phase transition. In all cases, the band gap increases with the alkali concentrations, whereby only the indium-based chalcopyrites reach the above-mentioned target values for applications in tandem photovoltaic devices. The static stabilities of the substituted materials have been further discussed in terms of substitution energies and energies of formation, with the latter being evaluated to secondary phases plausible in the process of synthesis. The comparison with the experimental situation and the impact of the novel predictions are discussed.