In addition to its role in chromosome maintenance, the six-membered Smc5/6 complex functions as a restriction factor that binds to and transcriptionally silences viral and other episomal DNA. However, the underlying mechanism is unknown. Here, we show that transcriptional silencing by the human Smc5/6 complex is a three-step process. The first step is entrapment of the episomal DNA by a mechanism dependent on Smc5/6 ATPase activity and a function of its Nse4a subunit for which the Nse4b paralog cannot substitute. The second step results in Smc5/6 recruitment to promyelocytic leukemia nuclear bodies by SLF2 (the human ortholog of Nse6). The third step promotes silencing through a mechanism requiring Nse2 but not its SUMO ligase activity. By contrast, the related cohesin and condensin complexes fail to bind to or silence episomal DNA, indicating a property unique to Smc5/6.