Low-dimensionality in magnetic materials often leads to noncollinear magnetic order, such as a helical spin order and skyrmions, which have received much attention because of envisioned applications in spin transport and in future data storage. Up to now, however, the real-space observation of the noncollinear magnetic order has been limited mostly to systems involving a strong spin-orbit interaction. Here we report a noncollinear magnetic order in individual nanostructures of a prototypical magnetic material, bilayer iron islands on Cu (111). Spin-polarized scanning tunnelling microscopy reveals a magnetic stripe phase with a period of 1.28 nm, which is identified as a one-dimensional helical spin order. Ab initio calculations identify reduced-dimensionality-enhanced long-range antiferromagnetic interactions as the driving force of this spin order. Our findings point at the potential of nanostructured magnets as a new experimental arena of noncollinear magnetic order stabilized in a nanostructure, magnetically decoupled from the substrate.