Mitochondrial outer- and inner-membrane fusion events are coupled in vivo but separable and mechanistically distinct in vitro, indicating that separate fusion machines exist in each membrane. Outer-membrane fusion requires trans interactions of the dynamin-related GTPase Fzo1, GTP hydrolysis, and an intact inner-membrane proton gradient. Inner-membrane fusion also requires GTP hydrolysis but distinctly requires an inner-membrane electrical potential. The protein machinery responsible for inner-membrane fusion is unknown. Here, we show that the conserved intermembrane-space dynamin-related GTPase Mgm1 is required to tether and fuse mitochondrial inner membranes. We observe an additional role of Mgm1 in inner-membrane dynamics, specifically in the maintenance of crista structures. We present evidence that trans Mgm1 interactions on opposing inner membranes function similarly to tether and fuse inner membranes as well as maintain crista structures and propose a model for how the mitochondrial dynamins function to facilitate fusion.