Although Martinez initially said he hoped Alcaraz would recover within 10 days, the Latics chief has accepted the South American will spend at least three weeks on the sidelines.
That is exactly the timeframe from the West Ham match until the Wembley showdown with Manchester City in Wigan's first FA Cup final.
As Alcaraz is such a key figure ni the Wigan defence, Martinez is bound to give him every opportunity to recover.
However, he accepts Alcaraz is cutting it fine.
"As it stands it would be difficult to tell," he said.
"We are talking about three weeks since it happened. It will be touch and go. It depends how quickly he can recover."
Club captain Gary Caldwell will step into the vacancy after being handed an unexpected recall at Upton Park.
Meanwhile, Martinez has confirmed midfielder Ben Watson, who broke his leg against Liverpool in November, is close to a first-team comeback following a couple of encouraging appearances in Wigan's Under-21 side.