Bottom-up synthetic biology aims to engineer artificial cells capable of responsive behaviors by using a minimal set of molecular components. An important challenge toward this goal is the development of programmable biomaterials that can provide active spatial organization in cell-sized compartments. Here, we demonstrate the dynamic self-assembly of nucleic acid (NA) nanotubes inside water-in-oil droplets. We develop methods to encapsulate and assemble different types of DNA nanotubes from programmable DNA monomers, and demonstrate temporal control of assembly via designed pathways of RNA production and degradation. We examine the dynamic response of encapsulated nanotube assembly and disassembly with the support of statistical analysis of droplet images. Our study provides a toolkit of methods and components to build increasingly complex and functional NA materials to mimic life-like functions in synthetic cells.