Grondona, president of the Argentine Football Association (AFA) since 1979, passed away on Wednesday at the age of 82.
He was reportedly taken to hospital after suffering a cardiac arrest, and it was confirmed shortly afterwards that he had been unable to recover.
As a result, the AFA announced that the opening round of fixtures, due to begin on Friday with Godoy Cruz taking on Banfield, had been postponed.
"The Argentine Football Association wishes to inform that following the death of president Julio Grondona, all official football activities are suspended," a statement read.
"The Argentine Football Association will resume administrative activities from Monday."