Di Santo suffered the injury following a tackle by Craig Gardner, who was dismissed for the foul.
Martinez told the Wigan Evening Post: "The cut swelled up straight away and it could be a little bit of ligament damage in his ankle and that is the worry. Obviously it was a very strong challenge. From where I was, his leading foot was really high and then he gets the ball with his second foot.
"Nowadays if you go into a challenge like that and it's a bit high, it's a reckless challenge with excessive force and a red card. I just saw Franco's leg and that's my worry. I need to see the extent of that injury. Franco had to come off and obviously he's got a couple of nasty cuts on his leg.
"The referee had a clear view and he was really on top of the incident. My worry is the extent of the injury."