Replication of positive-strand RNA viruses, the largest group of plant viruses, is initiated by viral RNA-dependent RNA polymerase (RdRp). Given its essential function in viral replication, understanding the regulation of RdRp is of great importance. Here, we show that Turnip yellow mosaic virus (TYMV) RdRp (termed 66K) is degraded by the proteasome at late time points during viral infection and that the accumulation level of 66K affects viral RNA replication in infected Arabidopsis thaliana cells. We mapped the cis-determinants responsible for 66K degradation within its N-terminal noncatalytic domain, but we conclude that 66K is not a natural N-end rule substrate. Instead, we show that a proposed PEST sequence within 66K functions as a transferable degradation motif. In addition, several Lys residues that constitute target sites for ubiquitylation were mapped; mutation of these Lys residues leads to stabilization of 66K. Altogether, these results demonstrate that TYMV RdRp is a target of the ubiquitin-proteasome system in plant cells and support the idea that proteasomal degradation may constitute yet another fundamental level of regulation of viral replication.