Italy will take on another World Cup-bound team, England, that same night in London.
Messi was reduced to the role of spectator at the Etihad Stadium, where goals from Ever Banega and Manuel Lanzini ensured the win for Jorge Sampaoli's men.
He said: "I have been suffering from this hamstring injury for some time".
A legendary Argentina striker has explained why FC Barcelona superstar Lionel Messi will never surpass Diego Maradona as the greatest footballer in Argentine football history. "We're on the right path", he said. We are playing well as a team, the philosophy is sensational...
Although Argentina and Italy have won six World Cups between them, there were large swathes of seats left empty as the Manchester public showed a lack of enthusiasm for two teams whose current squads are far from their finest vintage.
Buffon, winning his 176th cap, was quickly called into action as Di Maria tested the 40-year-old with a low strike.
The rest of the first half was played at a crawl with Argentina opportunities just before the interval for Leandro Paredes, Nicolas Tagliafico and Gonzalo Higuain all the crowd had to cheer.
His friend and Argentina team-mate Sergio Aguero is also injured and, despite light training with the national side, he will not play in Tuesday's match, having already missed the Italy game.
Insigne again came close then Caballero stopped an effort from Immobile before Argentina took control.
Caballero boosted his World Cup chances with good saves from Antonio Candreva and Insigne before Banega struck with a sweet left-foot shot from the edge of the area after 75 minutes.