DNA catenanes are assemblies made up of two or more DNA rings linked together through mechanical bonds, and they are desirable for engineering unique nanoscale devices. However, current methods of synthesizing DNA catenanes rely on the formation of strong linking duplexes between component units to enable interlocking and thus do not permit the synthesis of complex single‐stranded DNA structures with freely functioning units. We have recently reported DNA sequences that can thread through a DNA circle without the formation of a linking duplex. Here we show that these unique DNA molecules can be further used to make intricate symmetric or asymmetric DNA catenanes, single‐stranded DNA assemblies made up of a central mother ring interlocked to two identical or fraternal twin daughter rings, which have never been reported before. These addressable freely functioning interlocked DNA rings should facilitate the design of elaborate nanoscale machines based on DNA.