  We investigate minimal helix submanifolds of any dimension and codimension
immersed in Euclidean space. Our main result proves that a ruled minimal helix
submanifold is a cylinder. As an application we classify complex helix
submanifolds of $\mathbb{C}^n$: They are extrinsic products with a complex line
as a factor. The key tool is Corollary 1.3 which allows us to classify
Riemannian foliations of open subsets of the Euclidean space with minimal
leaves. Finally, we consider the case of a helix hypersurface with constant
mean curvature and prove that it is either a cylinder or an open part of a
hyperplane.
