In this study, we study the robust estimation for the copula parameter in semiparametric copula-based multivariate dynamic (SCOMDY) models proposed by Chen and Fan (2006). To this end, instead of the pseudo maximum likelihood estimator in Chen and Fan (2006), we use a minimum density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE is consistent and asymptotically normal under regularity conditions. We compare the performance between the two estimators when outliers exist through a simulation study.