The cell migration cycle proceeds with shaping the membrane to form new protrusive structures and redistribution of contractile machinery. The molecular mechanisms of cell migration are well-studied in 2D, but membrane shape-driven molecular migratory landscape in 3D fibrous matrices remains poorly described. 1D fibers recapitulate 3D migration, and here, we examined the role of membrane curvature regulator IRSp53 as a coupler between actin filaments and plasma membrane during cell migration on suspended 1D fibers. Cells attached, elongated, and migrated on the 1D fibers with the coiling of their leading-edge protrusions. IRSp53 depletion reduced cell-length spanning actin stress fibers, reduced protrusive activity, and contractility, leading to uncoupling of the nucleus from cellular movements. Using a theoretical model, the observed transition of IRSp53 depleted cells from rapid stick-slip migration to smooth, and slower migration was predicted to arise from reduced actin polymerization at the cell edges, which was verified by direct measurements of retrograde actin flow using speckle microscopy. Overall, we trace the effects of IRSp53 deep inside the cell from its actin-related activity at the cellular tips, thus demonstrating a unique role of IRSp53 in controlling cell migration in 3D.