The 22-year-old suffered the injury during the second half of Saturday's 1-0 win over Aldershot, which was his first game back in the side following four weeks out with a back injury.
Cresswell will go under the knife to have a metal plate and screws inserted in his shoulder and he now faces around eight weeks out of action, having initially being ruled out for three months.
"It seems like one thing after the other," Cresswell told BBC Radio Sheffield. "I just want to get this injury out of the way and get 2010 out of the way and start afresh.
"There are a lot of games coming up and to get a run in the side would've been great. This has come at a bad time and I am gutted. As a footballer all you want to do is play and I'm devastated.
"It could have been three months out but now its two months. I'm determined to be 100% fit in six weeks and back in the team in eight weeks."
Source: PA