Tour de France champion Wiggins, finished the 11th stage in the main pack behind winner Ramunas Navardauskas to stay fourth overall, two minutes five seconds behind leader Vincenzo Nibali.
"I'm not feeling very good at the moment, I've had a pretty rough 24 hours," Wiggins said.
"I've got a chest infection and a bog-standard head cold. Fortunately in these days, these kinds of stages, there's just a bit of fighting and you can get through them and hide a little bit.
"But I just want to try and fight through it and hope that in a few days' time I'll be all right.
"Most of the team have been sick," the Sky rider added. "It seems to last for three or four days and then you get better."
Wiggins went into the three-week race as one of the favourites but has suffered a series of mishaps including a bad downhill crash, being blocked behind another pile-up and suffering a puncture during the time trial.
On Tuesday's first full mountain stage, Wiggins lost 37 seconds to Italian Nibali and struggled on a steep section of the final climb.
Asked if the Giro d'ltalia was a tougher race than the Tour, Olympic time trial champion Wiggins retorted: "The Tour of Picardie is a bloody hard race if you get sick. There's only so much you can do."
Astana rider Nibali, who leads by 41 seconds from Australian Cadel Evans, with Sky's Rigoberto Uran third at 2:04, still considered Wiggins to be one of his big rivals for overall victory.
"Wiggins, Evans, Uran and (2011 Giro winner Michele) Scarponi are all my most serious rivals. And there's still a long way to go," he told Italian television.
The Giro d'Italia finishes in Brescia on May 26.
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- Vincenzo Nibali