Chronic hepatitis B virus infection is a leading cause of cirrhosis and liver cancer^,. Hepatitis B virus encodes the regulatory HBx protein whose primary role is to promote transcription of the viral genome, which persists as an extrachromosomal DNA circle in infected cells^,,. HBx accomplishes this task by an unusual mechanism, enhancing transcription only from extrachromosomal DNA templates. Here we show that HBx achieves this by hijacking the cellular DDB1-containing E3 ubiquitin ligase to target the ‘structural maintenance of chromosomes’ (Smc) complex Smc5/6 for degradation. Blocking this event inhibits the stimulatory effect of HBx both on extrachromosomal reporter genes and on hepatitis B virus transcription. Conversely, silencing the Smc5/6 complex enhances extrachromosomal reporter gene transcription in the absence of HBx, restores replication of an HBx-deficient hepatitis B virus, and rescues wild-type hepatitis B virus in a DDB1-knockdown background. The Smc5/6 complex associates with extrachromosomal reporters and the hepatitis B virus genome, suggesting a direct mechanism of transcriptional inhibition. These results uncover a novel role for the Smc5/6 complex as a restriction factor selectively blocking extrachromosomal DNA transcription. By destroying this complex, HBx relieves the inhibition to allow productive hepatitis B virus gene expression.