Doble, who enjoyed half an hour off the bench in last Friday's 2-2 draw at Bury, sustained the injury during training and was duly left out of Town's match-day 18 for the 2-2 Boxing Day draw at Notts County.
Manager Graham Turner told the club's official website: "He's broken a bone in his hand and I'm told it's a spiral fracture which is complicated.
"He was due to have it put in plaster and he could be out for somewhere between three and six weeks.
"It depends what sort of plaster cast they put on it. Some players play with a light one and so we'll have to see how that works out."
Doble, a Wales Under-21 international, has made four substitute appearances for Shrewsbury this season.