Corin said everybody on the beach wanted to touch and hold the dolphin and that no lifeguards came over to see what was happening.
He added that dead dolphins had also washed up on the beach the previous day.
The creature was a La Plata - or Franciscana - species, found in the waters around Argentina, Uruguay and Brazil.
With only 30,000 left in the world, it is considered to be a vulnerable species.
In the wake of the incident, The Argentine Wildlife Foundation said: "This occasion serves to inform the public about the urgent necessity to return these dolphins to the sea as soon as possible if they find them on the shore."