Balerdi was named in Argentina's 26-man squad last week after consistent performances with Olympique de Marseille, with whom he made 36 appearances across all competitions.
"Defender Leonardo Balerdi suffered a muscle injury in the soleus of his right leg and will not be able to be part of the squad that will play the World Cup," Argentina said in a statement.
"Hang in there, stay strong, and get well soon."
Argentina have not announced a replacement yet for the 27-year-old centre back who has 11 caps. They play Honduras in a friendly match later on Saturday.
The defending champions will open their Group J campaign against Algeria on June 16 before facing Austria and Jordan.