The Belgian rider, who won a stage of the Argentinean race last year, crashed during the finale of the second stage on Monday evening, colliding into the road with his face.
According to a medical report issued by the Lotto Soudal team, he lost one tooth and broke another one, and also suffered a fracture in the upper jaw and a cut to his upper lip.
Wallays was taken to a nearby hospital, where it was also established he had suffered concussion as a result of the impact. For that reason, he was forced to stay in hospital overnight for observation.
All being well, he will leave hospital and return to the teams hotel in San Juan today, before possibly catching an early return flight home.
Wallays is a key part of Lotto Soudal's classics squad, having previously won Dwars door Vlaanderen and Paris-Tours.
Stage 2 of the Vuelta a San Juan was won by Julian Alaphilippe (Deceuninck-QuickStep) with a late attack.