The 25-year-old suffered the problem on Sunday during his side's 33-20 defeat to Bradford Bulls in round five of the Challenge Cup.
Despite being cleared of a fractured ankle, Whitehead will be absent for the team's upcoming fixtures.
"It's a big loss for us," Dragons coach Laurent Frayssinous is quoted as saying by Sky Sports News.
"Elliott has been outstanding this season so far, but I am pleased for Elliott that it is not a fracture, as it was feared after the game. The medical staff will work closely with him now to make sure he rehabilitates correctly."
The Dragons return to Super League action on Saturday at home to Salford Red Devils.