Biomolecular condensation via phase separation of proteins and nucleic acids has emerged as a crucial mechanism underlying the spatiotemporal organization of cellular components into functional membraneless organelles. However, aberrant maturation of these dynamic, liquid-like assemblies into irreversible gel-like or solid-like aggregates is associated with a wide range of fatal neurodegenerative diseases. New tools are essential to dissect the changes in the internal material properties of these biomolecular condensates that are often modulated by a wide range of factors involving the sequence composition, truncations, mutations, post-translational modifications, and the stoichiometry of nucleic acids and other biomolecules. Here, we employ homo-Förster Resonance Energy Transfer (homoFRET) as a proximity ruler to study intermolecular energy migration that illuminates the molecular packing in the nanometric length-scale within biomolecular condensates. We used the homoFRET efficiency, measured by a loss in the fluorescence anisotropy due to rapid depolarization, as a readout of the molecular packing giving rise to material properties of biomolecular condensates. Using single-droplet anisotropy imaging, we recorded spatially-resolved homoFRET efficiencies of condensates formed by fluorescent protein-tagged Fused in Sarcoma (FUS). By performing single-droplet picosecond time-resolved anisotropy measurements, we were able to discern various energy migration events within the dense network of polypeptide chains in FUS condensates. Our homoFRET studies also captured the modulation of material properties by RNA, ATP, and post-translational modification. Additionally, we utilized mammalian cell lines stably expressing FUS to study nuclear FUS and oxidative stress-induced stress granule formation in the cytoplasm. Our studies demonstrate that spatially-resolved homoFRET methodology offers a potent tool for studying intracellular phase transitions in cell physiology and disease.