The Colombian, last year’s runner-up, hurt his left leg and arm during the chaotic and crash-ridden Stage 9.
He had hoped to recuperate on Monday’s rest day, but has elected to pull out after suffering on Tuesday's first mountain stage.
"Today I have to share some bad news," said Uran. "I didn’t recover after the crash. Yesterday in the first real climb, all day, there was pain in my body."
Uran sat 30th in the General Classification, over 30 minutes adrift of Team Sky pacesetter Geraint Thomas.
"The most important thing is the rider’s health," said Cannondale head sport director Charly Wegelius.
"Rigo hasn’t recovered from his crash on the cobbled stage, and his position on the bike is compromised and could create further issues down the line. We along with Rigo felt it best to pull out of the Tour this morning so he can recover and look toward the remainder of the season.
"Ultimately this decision comes down to the rider. If a rider wants to continue the race, we look to ways to do that safely. If a rider feels it best to pull out, we do not push them to continue."