Mathare MP Anthony Oluoch has fractured his leg as police dispersed protesters in the area.
Residents were protesting after five people were shot dead by unknown assailants on on Saturday night.
Police fired tear gas at residents who have denied them access to the scene and two vehicles were burnt in retaliatory attacks.
"The police with no provocation opened fire on us and shot tear gas canisters. In the melee, Oluoch suffered a multiple compound fracture of the left leg," NASA said in a statement.
Police spokesperson Japhet Koome has said the killings were a criminal act and not from ethnic profiling.
Opposition leader Raila Odinga visited Riverside and is expected at the Nairobi Hospital where the MP was rushed to.
More to follow
