The 28-year-old is out with ankle ligament damage picked up during the first half of Saturday`s 3-0 defeat to Bristol City.
Jordan, who signed for the Blades after his release by Burnley in the summer, is no stranger to injury problems having suffered three disrupted seasons with the Clarets due to various niggles.
United boss Gary Speed told the Sheffield Star: "Stephen is going to be missing for quite a while unfortunately.
"We were keeping our fingers crossed that it wouldn't be too bad but the usual timescale for this type of thing is just over a month."
Source: PA
Source: PA