The Spaniard, a Tour winner in 2007 and 2009, crashed during the 10th stage on Monday but then remounted his bike to pedal a further 15 kilometres before the pain got unbearable.
"Alberto Contador chose the Clinica Centro after contacting Real Madrid FC and more specifically Emilio Butragueno, with whom he enjoys a good relationship," his spokesman said in a statement.
"Butragueno quickly got to talk to the club's medical services and they in return recommended to consult with Dr. Leyes, a specialist in the type of injury suffered by the leader of Tinkoff-Saxo."
The kind of injury Contador suffered usually requires at least six weeks of recovery.
The Vuelta starts on August 23.
Several top names are expected to take part in the Vuelta, including 2013 Tour champion Chris Froome, who pulled out of this year's race after a crash last week.
(Reporting by Julien Pretot; editing by Pritha Sarkar)
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