The Stade Francais fly-half had scored two penalties when he suffered the blow to the wrist after 18 minutes and was forced to leave the field.
An Argentinian Rugby Union statement confirmed Hernandez suffered a fracture of the trapezium bone in his right hand and will undergo surgery in Buenos Aires.
"I wanted to play the whole match; sadly I didn't last long," said Hernandez. "I am angry because of the injury but I think I will have time to rest now after two long years of competitions. I have been forced to rest, but I am going to return stronger than ever."