  We consider a two-dimensional model of viscoelastic von K\'arm\'an plates in
the Kelvin's-Voigt's rheology derived from a three-dimensional model at a
finite-strain setting. As the width of the plate goes to zero, we perform a
dimension-reduction from 2D to 1D and identify an effective one-dimensional
model for a viscoelastic ribbon comprising stretching, bending, and twisting
both in the elastic and the viscous stress. Our arguments rely on the abstract
theory of gradient flows in metric spaces by Sandier and Serfaty and complement
the $\Gamma$-convergence analysis of elastic von K\'{a}rm\'{a}n ribbons in
[Freddi et al., 2018]. Besides convergence of the gradient flows, we also show
convergence of associated time-discrete approximations, and we provide a
corresponding commutativity result.
