Argentina struggled against Iran at Belo Horizonte's Mineirao stadium on Saturday with Maradona in the stands as a spectator along with his daughter.
The 1986 World Cup winner got out of his seat and left shortly before the end of both halves, missing Lionel Messi's brilliant stoppage-time winner which gave them a 1-0 win and a place in the 16.
"Jinx this," Maradona said, looking at the camera of Venezuela's Telesur broadcaster for whom he works as a commentator at the World Cup and holding up his middle finger in response to Grondona's comments to reporters.
"Poor, stupid man. This is Messi's merit, Not because I left," Maradona added.
Telesur is a left-leaning Caracas-based Latin American network set up by the late socialist leader Hugo Chavez as an intended counterpoint to what he saw as capitalist-dominated global media.
Maradona was an admirer and friend of Chavez's, as well as Cuba's former leader Fidel Castro.
The 82-year-old Grondona, who has been head of the Argentina FA since 1979, was in charge when Maradona almost single-handedly steered Argentina to World Cup victory in Mexico in 1986.
Maradona was coach of the national team at the last World Cup in 2010.