Living cells have the ability to control the dynamics of responsive assemblies such as the cytoskeleton by temporally activating and deactivating inert precursors. While DNA nanotechnology has demonstrated many synthetic supramolecular assemblies that rival biological ones in size and complexity, dynamic control of their formation is still challenging. Taking inspiration from nature, we developed a DNA-RNA nanotube system whose assembly and disassembly can be temporally controlled at physiological temperature using transcriptional programs. Nanotubes assemble when inert DNA monomers are directly and selectively activated by RNA molecules that become embedded in the structure, producing hybrid DNA-RNA assemblies. The reactions and molecular programs controlling nanotube formation are fueled by enzymes that produce or degrade RNA. We show that the speed of assembly and disassembly of the nanotubes can be controlled by tuning various reaction parameters in the transcriptional programs. We anticipate that these hybrid structures are a starting point to build integrated biological circuits and functional scaffolds inside natural and artificial cells, where RNA produced by gene networks could fuel the assembly of nucleic acid components on demand.