Phase separation of biomolecules plays key roles in physiological compartmentalization as well as pathological aggregation. A deeper understanding of biomolecular phase separation requires dissection of a relation between intermolecular interactions and resulting phase behaviors. DNA nanostars, multivalent DNA assemblies of which sticky ends define attractive interactions, represent an ideal system to probe this fundamental relation governing phase separation processes. Here, we use DNA nanostars to systematically study how structural flexibility exhibited by interacting species impacts their phase behaviors. We design multiple nanostars with a varying degree of flexibility using single-stranded gaps of different lengths in the arm of each nanostar unit. We find that structural flexibility drastically alters the phase diagram of DNA nanostars in such a way that the phase separation of more flexible structures is strongly inhibited. This result is not due to self-inhibition from the loss of valency but rather ascribed to a generic flexibility-driven change in the thermodynamics of the system. Our work provides not only potential regulatory mechanisms cells may exploit to dynamically control intracellular phase separation but also a route to build synthetic systems of which assembly can be controlled in a signal dependent manner.