The Team Sky captain had been one of the top favourites to win the race, but a combination of crashes, bad weather and illness have forced him to throw in the towel.
Team Sky manager Dave Brailsford confirmed the news in a statement on the team's website.
“We monitored Bradley overnight and this morning we’ve withdrawn him from the Giro after consulting the team doctor. His chest infection has been getting worse and our primary concern is always the health of our riders," he said.
“Bradley will return to the UK today for treatment and to rest and we hope to have him back on the road as soon as possible. As a passionate racer he wanted to continue but he is simply unable to do so on medical grounds.”
Wiggins admitted on Wednesday that he was suffering from a respiratory infection and a cold. The cooler temperatures and heavy rainfall during Thursday's stage to Treviso proved too much for him. Wiggins dropped back on the final descent of the day, was unable to stay with the peloton on the flat and eventually crossed the finish line 3:17 behind winner Mark Cavendish (Omega Pharma-Quick Step).
Team Sky will now look to Rigoberto Uran to lead the British squad at the Giro d'Italia. The Colombian is in third place overall, 2:04 down on Nibali.
Friday's thirteenth stage is a almost totally flat 254km ride across northern Italy from Busseto to Cherasco.