Dynamin 1-like proteins (DNM1-L) are mechanochemical GTPases that induce membrane fission in mitochondria and peroxisomes. Their mechanism depends on conformational changes driven by nucleotide and lipid cycling. Here we show the crystal structure of a mitochondrial fission dynamin (CmDnm1) from the algae Cyanidioschyzon merolae. Unlike other eukaryotic dynamin structures, CmDnm1 is in a hinge 1 closed conformation, with the GTPase domain compacted against the stalk. Within the crystal, CmDnm1 packs as a diamond-shaped tetramer that is consistent with an inactive off-membrane state. Crosslinking, photoinduced electron transfer assays, and electron microscopy verify these structures. In vitro, CmDnm1 forms concentration-dependent rings and protein–lipid tubes reminiscent of DNM1-L and classical dynamin with hinge 1 open. Our data provides a mechanism for filament collapse and membrane release that may extend to other dynamin family members. Additionally, hinge 1 closing may represent a key conformational change that contributes to membrane fission.