Maradona, widely considered one of the greatest footballers of all time, passed away on Wednesday.
The Argentine president declared three days of national mourning.
The 1986 World Cup winner and the national team's former manager had been in hospital in Buenos Aires after surgery to remove a blood clot on the brain earlier this month.
He was being treated for alcohol dependency.
The AFA said on Twitter: "The Argentine Football Association, through its president Claudio Tapia, expresses its deepest sorrow for the death of our legend, Diego Armando Maradona. You will always be in our hearts."
Maradona's successes made him a global star and a national hero in Argentina but his career was also blighted by controversies on and off the field.
His 'Hand of God" goal against England in the 1986 quarter-finals, when he pushed the ball into the net with his hand, earned him infamy - although he followed up by scoring the "goal of the century", a remarkable solo effort, in the same game.
His international playing career ended in shame when he failed a drugs test at the 1994 World Cup in the United States and he was notorious for a wayward lifestyle.
He was also banned from football in 1991 after testing positive for cocaine while playing for Napoli.
During his club career, he was most associated with Boca Juniors, Barcelona and the Italian club, where he won two Serie A titles, including their first ever, to write himself into the Napolese folklore.
"We are in mourning," said club spokesman Nicola Lombardo. "We feel like a boxer who has been knocked out. We are in shock."
The attacking midfield scored 34 goals in 91 appearances for Argentina, representing them in four World Cups and captaining them to glory in Mexico '86 with a series of sublime performances.
He also led La Seleccion to the final in Italy four years later, where they were beaten by West Germany, but the troubles that would plague him after retirement were apparent at USA '94, where he was sent home for testing positive for ephedrine.
Struggles with addiction would colour the latter part of his career and his time after football, during which he held a variety of managerial roles.
He officially retired as a player on his 37th birthday, October 30 1997, during a second stint with Boca.
Having briefly been a player manager with two Argentine sides, he was appointed head-coach of the national team in 2008, departing two years later after their defeat by Germany in the quarter-final of the 2010 World Cup.
He went on to manage teams in the United Arab Emirates and Mexico and was in charge of Gimnasia y Esgrima in Argentina's top-flight at the time of his death.