We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higher-order correlation effects like biexcitons in optical processes in solids based on a reduced two-particle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schrödinger equation for biexcitons in terms of one- and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model.