McCarthy was carried off on a stretcher after a heavy tackle from Bolton's Fabrice Muamba in Saturday's Premier League clash at the DW Stadium.
The injury is not as bad as the club initially feared but McCarthy still faces a lengthy lay-off.
Martinez said: "It is a little bit better than we thought at first but it is obviously ligament damage in the right ankle.
"When it is swollen it is sometimes difficult to assess but there is no fracture, we hope.
"We expect to get the results of the scan today and then hopefully it will be eight to 10 weeks."
Martinez was unhappy with Muamba's tackle on the 19-year-old, labelling the fact it has resulted in a spell on the sidelines a "football crime".
The Spaniard said: "It was a completely unnecessary challenge.
"Obviously it was not malicious at all but it was reckless.
"It was one of those challenges where only one person can get hurt and that was someone who wants to get on the ball and try to be creative.
"It is an incident that is going to happen in football, it is just that thin line - if the referee feels it was reckless or with excessive force it can be a red card.
"But what worries me more is the health of James McCarthy.
"Probably one of the most creative young players in the Premier League is going to be out for up to 10 weeks. That is a football crime."
Martinez has no doubt the club will miss the in-form Republic of Ireland international, who has made a big impression since his move from Hamilton last year.
"He has been sensational," Martinez said. "Sometimes it is hard to understand the age of James.
"He plays with a great maturity and understanding and the level of performance has been so consistent for a young man it shows you the quality he has got.
"When he was stretchered off I feared the worst but, I know eight to 10 weeks is a long time, but we will use that period to try to refresh him.
"When he comes back he will be stronger and ready to make a real impact in the rest of the season."
Defender Emmerson Boyce is also likely to be out for two to three weeks with a pulled hamstring.