This study is aimed to calculate the radiative lifetime of Wannier-Mott excitons in nanoclusters of a narrow-bandgap semiconductor embedded in a wide-bandgap one. The nanocluster linear dimensions are assumed to be much larger than the radius of the exciton so that the latter is not destructed by the confinement potential as it takes place in small quantum dots. The calculations were carried out for an example of InAs nanoclusters put into the GaAs matrix. It is shown that the radiative lifetime of Wannier-Mott excitons in such clusters increases with the decrease of the cluster dimensions, this tendency being more pronounced at low temperatures. So, the creation of excitons in nanoclusters of a narrow-bandgap material embedded in a wide-bandgap one can be used to significantly prolong their radiative lifetime in comparison with that of excitons in a bulk semiconductor.