A spokeswoman for the Metropolitan police said police were called to the hospital at about 13:50 BST yesterday.
She added that no arrests have been made and no suspect descriptions are available.
Scotland Yard's black-on-black crime unit, Operation Trident, is investigating the shooting, which comes at a time of heightened concern about levels of gun crime in the capital.
A police cordon has been set up along Nicol Road and some local residents have been stopped from returning to their homes.
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