Sir Bradley has already left the competition to fly home to recover from a severe chest infection.
He had been struggling throughout the Giro, both on rainy descents and on steep climbs.
The seven-times Olympic medallist lost more than three minutes on Thursday during a rainy stage and left the race in 13th place – five minutes and 22 seconds behind overall leader Vincenzo Nibali.
As a passionate racer he wanted to continue but he is simply unable to do so on medical grounds.Team Sky
Team Sky said that Wiggins had made his decision on the advice of the team physician due to “a worsening chest infection.”
“We monitored Bradley overnight and this morning we’ve withdrawn him from the Giro after consulting the team doctor,” said Team Sky General Manager Dave Brailsford.
“His chest infection has been getting worse and our primary concern is always the health of our riders. 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.”
Tour de France
“As a passionate racer he wanted to continue but he is simply unable to do so on medical grounds,” Mr Brailsford added.
By leaving the competition halfway through, Wiggins will hope to be back on form in time for the Tour de France, which begins on 29 June.