The Chesterfield-born player, who has an Italian father, damaged his knee while playing for the Italy Under-18s against Austria last week and is to have a scan to determine the full extent of the injury.
De Girolamo, 17, had been in contention for his first start for the Blades after making substitute appearances in recent home games against Colchester and Leyton Orient.
"Diego will have scan on March 20 to confirm what we feel about the problem," Wilson told a press conference ahead of Tuesday night's game at Crewe.
"He isn't going to play for a while, but we don't know how long he will be out for at the moment and I'm not prepared to speculate.
"It isn't fair on the lad without knowing all the facts, but he will certainly be missing for the next few weeks, minimum.
"We're all gutted for him, especially with him being a young lad.
"He has got everything in front of him, but all that excitement has been taken away from him now.
"He would have relished the opportunity to feature in the run-in. But this injury is how football is and he will have the support of the club throughout his recovery."
- Sports & Recreation