The England international, who has missed much of the season after damaging knee ligaments during a pre-season tour of the United States, suffered pain and bruising in his foot after Chelsea's 1-1 draw at Manchester United last month.
"When the pain failed to subside, today's scan was carried out," the English champions said on their Web site www.chelseafc.com.
"Cole, who has been reduced to just three starts and eight substitute appearances this season...will now miss the busy Christmas programme," Chelsea added.