Holden, 25, suffered a knee injury in a challenge with Manchester United's Jonny Evans on Saturday at Old Trafford. The Bolton midfielder, who absolved Evans from blame, will miss some key games for club and country including the FA Cup semi-final against Stoke.
He is also ruled out of the United States home friendlies against Argentina on Saturday and Paraguay next week as well as the Gold Cup in June. Bradley will keep a keen eye on Holden's progress. In a message to Press Association Sport from the squad's training camp in Cary, North Carolina, he said: "We all feel really bad for Stuart because obviously he got injured last year when we played Holland.
"Now he's had an excellent season at Bolton and is a player we see as being an important part of our team. We were looking forward to having him with us at 100% and confident. This is a setback but he's shown in the past the mentality to fight through these things. He knows we're all behind him."
Holden revealed on his Twitter account that surgery on his injured knee was a success. He said he had been given a big lift and encouragement by "overwhelming messages of support".
Club captain Kevin Davies was one of those who raised his spirits, saying on Twitter: "I am gutted for Stuart. He is a young, strong boy and our great medical team will have him ready for next season."