Maradona's death was confirmed by Argentina's football association on Wednesday.
He had been in hospital in Buenos Aires after surgery to remove a blood clot on the brain earlier this month.
Maradona captained his country to World Cup glory in Mexico in 1986, and later led Napoli to two Serie A titles in 1987 and 1990. He also coached the Argentine national team (and Messi) from 2008 to 2010.
Messi is widely regarded as Argentina’s heir to Maradona given his diminutive stature, dribbling ability and success with Barcelona, and the pair are recognised as two of - if not the two - greatest players ever.
Barca captain Messi took to Instagram following the news of Maradona’s passing to pay tribute to his former coach.
Messi wrote: "A very sad day for all Argentines and for football.
"He leaves us but does not leave, because Diego is eternal.
"I keep all the beautiful moments lived with him and I wanted to take the opportunity to send my condolences to all his family and friends. RIP."
Barca also paid tribute, tweeting: “FC Barcelona expresses its deepest condolences regarding the death of Diego Armando Maradona, a player for our club (1982-84) and an icon of world football.
"Rest in peace Diego”.
Additional reporting by PA.