The micellization in a selective solvent of a diblock copolymer with blocks of different stiffness is studied with Monte Carlo simulation on a cubic lattice. When the stiffness of the insoluble block increases, the critical micelle concentration (cmc) decreases and the averaged micelle size increases. On the other hand, an increase in the stiffness of the soluble block does not affect the micellization process to any appreciable extent. The decrease in the cmc when the stiffness of the insoluble block increases is interpreted as arising from the conformational contribution to the effective chi parameter. We interpret this contribution as being due to an increased number of heterocontacts between the insoluble block and the solvent molecules when the stiffness of the insoluble block increases.