The former Portsmouth striker suffered an exposed fracture of the leg after his pick up truck collided with a lamp-post.
"There was no other solution other than to amputate below the knee," said Mario Cancela, head of the intensive care unit at the private hospital where Silva is staying.
"He's stable, he's lucid and he's told me how the accident happened," added Cancela.
"This has encouraged us because from an encephalic point of view, it means he should make an almost complete recovery."
Silva, who was in an induced coma until Monday morning, was not yet aware of the amputation.
Silva played in the English Premier League last year for Portsmouth last year, but was currently out of contract.
The 33-year-old striker began his career with local side Defensor Sporting and then joined more fashionable Penarol.
He moved to Europe in 1995 to play for Italy's Cagliari and has since played for Espanyol, Malaga and Sevilla in Spain before his stint in England.
Silva made 49 appearances for Uruguay between 1995 and 2005, scoring 14 goals, and played at the 2002 World Cup, when Uruguay were knocked out in the first round.