Kensington and Chelsea council said it had given the owner a section 215 notice ordering the stripes' removal after neighbours complained.
The stripes appeared earlier this month after plans to demolish the house and replace it with a new house and two-storey basement were refused.
Neighbours said it looked "hideous".
The house, in a quiet cul-de-sac, must be repainted by 3 July.
The owner has until 5 June to appeal the decision.
A council spokesman said: "The property is situated within the Kensington Square Conservation Area and its condition and appearance has attracted numerous complaints to the council's planning enforcement team."
A woman in Kensington has been told to remove the red and white stripes she had painted on her house in protest over a rejected planning application.