Quintana, who was one of the favourites to win the race, was forced out on Thursday after a second crash in as many days
Quintana led the race going into Tuesday's 10th stage time trial, but lost time after going over his handlebars while trying to adjust his pedal clips on a descent.
And though the Colombian survived that crash, another incident on Wednesday's 11th stage saw him go out of the race with a drill-hole fracture of the coracoid process on his shoulder blade.
"This kind of fracture is really rare," explained Movistar Team doctor Alfredo Zúñiga.
"The coracoid process can be treated without any operation, but I decided to have him undergo surgery because, as shown on the scanner image, the fracture extends like the tail of a mouse to the scapula - we fixed it with two screws.
"The normal process would be keeping his right arm in a sling for two to three weeks.
"Then, he would be able to move it; after that, he could be getting on his bike fast, in two to four weeks, and after 6-8 weeks, he could start competing. All of that, with no complications in these 48 hours after surgery with infections or any acute pain. Nairo showed humble, calm and didn't complain about anything; it was all easy with him, he's a charming kid."
Quintana should be able to leave hospital on Friday.
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