Cudicini was forced off with a hamstring injury and joins Petr Cech on the sidelines following the first-choice goalkeeper's facial injury sustained in training.
Grant said: "The news is that is doesn't look so good for the moment with Carlo but we need to wait and see. It is his hamstring.
"This year I am more a doctor than a manager, I need to answer every week about injuries."
The injury means Rhys Taylor, 18 earlier this week, could be on the bench against Wigan on Monday.
Grant added: "Hilario was good today. It is very important for a third goalkeeper when you need him, and we have needed him this year, for him to do a good job. It's not easy when you lose your goalkeeper.
"We Hilario and have the goalkeeper from the youth team. He is a good goalkeeper."