Walker, currently the leading points scorer in the Guinness Premiership, is set to miss the league away clash at Harlequins this weekend with the injury.
However, Director of Rugby Mike Ruddock is confident the 31-year-old could make a return in time for the home clash with Leicester Tigers later this month.
"Today we've received some bad news in the form of an injury to Willie Walker," said Ruddock.
"Willie has sustained a fracture to a bone in his hand and it means we will be without him for around four weeks of the league campaign.
"There are no complications in terms of the injury or the fracture and so I fully expect him to be in the mix for our home league game against Leicester Tigers on Saturday, March 27.
"In the meantime, we have every confidence that Matthew Jones will step up to the plate and show us the qualities that he has as an international No.10.
"Matthew has been very patient since recovering from his own foot injury and is desperate for this opportunity to show his skills."
