Sanchez beat Italy's Davide Rebellin to top the Olympic podium in China four years ago after a tough, 245-km road race from the Forbidden City in ancient Beijing to the Great Wall.
"Although he is in good physical shape, he is still suffering a certain amount of pain in his hand and shoulder," Spanish team coach Jose Luis De Santos said.
"He was struggling to hold the handlebars and to change gears which could have been dangerous in a race. For this we have decided he won't go to London."
Sanchez was forced to abandon the Tour after breaking his hand and suffering a shoulder injury on the eighth stage just over a week ago.
The Euskaltel-Euskadi rider briefly lost consciousness following the incident and afterwards was diagnosed with a hand fracture and trauma to the left shoulder.
After a test run on Thursday, De Santos said he had discussed the matter with Sanchez and taken the decision.
"(I want to) thank Samuel for the great effort he has put in to try and be at the Games and in a race as important to him as defending champion as it is for everyone else," De Santos said.
"He has shown a great deal of pride in a difficult situation and I hope he can recover as soon as possible."
De Santos said he would propose Jonathan Castroviejo as a replacement to the Spanish Olympic committee.
The road race at the London Games takes place on July 28.
Sanchez is the second Spanish defending Olympic champion to withdraw on Thursday, with tennis star Rafael Nadal also pulling out citing fitness problems.