According to The Guardian, the striker - named on Monday in Stuart Pearce's Great Britain squad for the Games - was taken ill over the weekend and is being treated by Chelsea's medical staff.
Pearce's squad is due to meet up at a training camp at Loughborough this weekend before heading off for training in Spain.
It is not yet clear how serious the illness is, but Pearce may have to call on a replacement for Sturridge if he does not recover quickly.
Pearce has until 25 July to call up a replacement, with Britain's first match the next day against Senegal at Old Trafford.
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