FtsZ is a self-assembling GTPase that forms, below the inner membrane, the mid-cell Z-ring guiding bacterial division. FtsZ monomers polymerize head to tail forming tubulin-like dynamic protofilaments, whose organization in the Z-ring is an unresolved problem. Rather than forming a well-defined structure, FtsZ protofilaments laterally associate in vitro into polymorphic condensates typically imaged on surfaces. We describe here nanoscale self-organizing properties of FtsZ assemblies in solution that underlie Z-ring assembly, employing time-resolved x-ray scattering and cryo-electron microscopy. We find that FtsZ forms bundles made of loosely bound filaments of variable length and curvature. Individual FtsZ protofilaments further bend upon nucleotide hydrolysis, highlighted by the observation of some large circular structures with 2.5-5° curvature angles between subunits, followed by disassembly end-products consisting of highly curved oligomers and 16-subunit -220 Å diameter mini-rings, here observed by cryo-electron microscopy. Neighbor FtsZ filaments in bundles are laterally spaced 70 Å, leaving a gap in between. In contrast, close contact between filament core structures (∼50 Å spacing) is observed in straight polymers of FtsZ constructs lacking the C-terminal tail, which is known to provide a flexible tether essential for FtsZ functions in cell division. Changing the length of the intrinsically disordered C-tail linker modifies the interfilament spacing. We propose that the linker prevents dynamic FtsZ protofilaments in bundles from sticking to one another, holding them apart at a distance similar to the lateral spacing observed by electron cryotomography in several bacteria and liposomes. According to this model, weak interactions between curved polar FtsZ protofilaments through their the C-tails may facilitate the coherent treadmilling dynamics of membrane-associated FtsZ bundles in reconstituted systems, as well as the recently discovered movement of FtsZ clusters around bacterial Z-rings that is powered by GTP hydrolysis and guides correct septal cell wall synthesis and cell division.