  We study minimal cylinders in the three-dimensional Heisenberg group ${\rm
Nil}_3$ using the generalized Weierstrass type representation, the so-called
loop group method. We characterize all non-vertical minimal cylinders in terms
of pairs of two closed plane curves which have the same signed area. Moreover,
as a byproduct of the construction, spacelike CMC cylinders can also be
obtained.
