The optical properties of bare and passivated Znn Sen (n=1-13) clusters have been studied within the framework of time-dependent local density approximation. The atomic structure of the clusters has been obtained using projector augmented wave pseudopotential method, with generalized gradient approximation for the exchange-correlation energy. The small clusters with n up to 5 have two-dimensional (2D) structure and for larger sizes, cagelike 3D structures become favorable. At n=13, the clusters start getting an atom inside the cage to attain bulklike local structure. For the bare clusters, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap increases from a small value for ZnSe dimer and beyond n=3, the variation is small. On the other hand, the HOMO-LUMO gap of the clusters passivated with partially charged hydrogen atom decreases nearly monotonically with increasing size, though the value remains higher compared with that of the bare clusters even for the case of n=13. Further, the optical absorption spectra and the corresponding optical gap have been calculated and a decreasing trend as a function of the increasing cluster size has been obtained. This compares well with the experimental results available on larger clusters in the literature though the calculated values underestimate the optical absorption gap as expected within the local density approximation framework. {\textcopyright} 2009 The American Physical Society.