It's a first top-four scalp for Cuevas, who will face Lucas Pouille in the quarters after overcoming Wawrinka 6-4 6-4.
The Swiss world number three lost his opening serve in both sets, while he also failed to make a break point opportunity on the Cuevas serve.
The upset follows Andy Murray's 6-2 2-6 5-7 defeat to Albert Ramos-Vinolas, with the world No. 1 throwing away a 4-0 third-set lead.
Read the original article on Eurosport: No. 3 seed Wawrinka dumped out of Monte Carlo by Cuevas