Competing risks data commonly arise when an occurrence of an event precludes other type of events from being observed. Recently, competing-risks models with frailty have been studied for clustered competing-risks data that may be correlated. In this paper, we propose a variable selection procedure for fixed effects in the cause-specific hazard frailty model for the clustered competing-risks data using a penalized likelihood. Here we consider two popular penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD). We derive simple matrix forms for the variable selection procedure. The usefulness of the proposed method is illustrated using a practical example data set.