Di Santo joined the Latics in the summer of 2010 from Chelsea having managed only a single goal in English football while on loan at Blackburn.
But he finished last season as the club's top scorer and has netted three times so far this term, prompting recognition from Argentina boss Alejandro Sabella.
Martinez said: "We always had a huge belief in Franco, we always saw his potential. The chairman made a massive investment in him and since then his application and his desire to fulfil his potential has been very important.
"To get an Argentina cap is a huge achievement. We should never forget the players that he's going to have in that squad. For us it's a great feeling of pride. We're all very, very proud of what Franco has achieved.
"It's been a target of his and it's an incredible journey he's been on. He arrived here as a young man with great potential, now he's a proper footballer, a top player.
"You look at the squad and you've got players from Barcelona, Real Madrid,
Manchester City and Wigan in that forward line, and that's a real compliment for everybody at the football club but especially Franco.
"We're all very excited about what the next level will bring because he's ready to be an important player in the Argentina squad and that's the next step for him."
Di Santo, who should return for Wigan's trip to Tottenham on Saturday after being rested against Brentford in the League Cup, has been named in Sabella's 23-man line-up for the friendly against Saudi Arabia in Riyadh on 14 November.