Basso, 35, woke with “an uncomfortable swelling” on Wednesday and, after consulting the Team Cannondale doctor, has been forced to pull out of the Tour, which starts in Naples on Saturday.
“After a new evaluation, it was clear that Basso would be totally unable to pedal during the coming days,” the team said. “Cannondale Pro Cycling called upon Damiano Caruso to take his place.”
Wiggins will be Team Sky’s only British representative in Italy, as Chris Froome continues preparations for the Tour de France, which begins in June.
The event will cover 3,405km and concludes in Brescia with a final road stage on 26 May.