Sabella, who led his country to the World Cup final in 2014, had been ill in hospital in his homeland.
The Argentina Football Association (AFA) said in a Twitter statement: "The AFA, via president Claudio Tapia, deeply regrets the death of Alejandro Sabella, former coach of Argentina, and sends its warmest hug to his family and loved ones."
A former international midfielder who played for Sheffield United and Leeds United in England, as well as River Plate and Estudiantes, he was best known for his work as a coach towards the end of his career in football.
Sabella led Estudiantes to Copa Libertadores glory in 2009 and the final of the Club World Cup later that year, where they lost to Pep Guardiola's Barcelona.
Hugely popular in La Plata, Sabella took over as national team boss from Sergio Batista in 2011.
Appointing Lionel Messi as captain, the Albiceleste reached the final of the World Cup six years ago in Brazil, where they lost 1-0 to Germany thanks to Mario Gotze's extra-time goal. Messi was awarded the Golden Ball as the tournament's best player.
Sabella resigned from his position in July 2014, having suggested he no longer had the energy to fulfil the demands of the role.
Estudiantes described Sabella as "the star that we choose and will wear proudly on our chest", adding: "Thank you for so many teachings and for your legacy."
Radamel Falcao, who knew Sabella from his early career with River, wrote on Twitter: "Unfortunate news of the death of Alejandro Sabella. We worked together at River.
"My condolences to his family, friends, and everyone who had the opportunity to know him."
Mascherano, 36, revealed his decision on Sunday, calling it quits after 17 years as a professional.
A 147-time Argentina international – the most in the country's history – Mascherano returned to his homeland by signing with Estudiantes de La Plata in January.
After 11 appearances in all competitions for the Argentine side, including Sunday's 1-0 loss to Argentinos Juniors, Mascherano said it was time to hang up his boots.
"I want to announce that today I am retiring from football professionally," he said.
"I want to thank this club that gave me the opportunity to finish my career in Argentina."
Mascherano added: "I have lived my profession 100 per cent, I gave the maximum I could.
"Today, I find that for some time it's hard for me and I don't want to disrespect Estudiantes, who trusted me to return to Argentina, or my colleagues, or this profession."
After beginning his career with River Plate, Mascherano played for Corinthians and West Ham before joining Liverpool in 2007.
A fearless defensive midfielder who turned into a centre-back, Mascherano enjoyed most of his success at Camp Nou, winning five LaLiga titles and the Champions League twice among numerous other trophies after joining Barca in 2010.
He helped Argentina reach the 2014 World Cup final, which they lost to Germany in extra time, while finishing with four Copa America runner-up medals and two Olympic golds.
After two years with Hebei China Fortune, Mascherano headed back to Argentina with Estudiantes, where he finished his career.
The Premier League leaders have been heavily linked with a move for RB Leipzig forward Timo Werner.
However, they may instead be looking at a Premier League star.
TOP STORY – LIVERPOOL WANT TRAORE
Liverpool want to add Wolves attacker Traore this close season, according to The Sun.
Traore had scored four goals and provided seven assists in 28 Premier League games before this season was suspended due to the coronavirus pandemic.
The 24-year-old arrived in England from Barcelona in 2015, playing for Aston Villa and Middlesbrough before joining Wolves.
ROUND-UP
- Following reports Paris Saint-Germain had made a bid for Mauro Icardi, who is on loan at the club from Inter, it seems that may not be the case just yet. L'Equipe says PSG and Inter are still in negotiations over the forward, with the Ligue 1 side hoping to pay less than the €70million purchase option they hold.
- Samuel Umtiti's future at Barcelona remains unclear. Marca says the defender will not leave the LaLiga giants, while Sport reports Inter could be prepared to sign the centre-back.
- Manchester City and Barcelona could be set for a deal. The Sun reports City see Nelson Semedo as a good option to provide competition for Kyle Walker, while Joao Cancelo could be offered in a potential deal.
- On loan at Estudiantes, Marcos Rojo appears likely to leave Manchester United permanently. The Mirror says the Premier League club are hoping Boca Juniors and Estudiantes enter a bidding war for the 30-year-old.
- Everton are said to be interested in Jean-Clair Todibo, who is on loan at Schalke from Barcelona this season. Sport reports the Premier League club have offered £19.7million (€22m) plus £2.7m (€3m) in variables for the defender.
