A plan to build an Apple store at Federation Square has been shelved, after heritage authorities refused an application to demolish part of the existing square.

Apple will not proceed with its plan, and the Andrews government will now review the operation of Federation Square.

The Koorie Heritage Trust, which includes an Aboriginal art gallery, was to make way for Apple and be relocated elsewhere in the square. It will instead remain where it is, for now.

The Yarra building at Federation Square will not be demolished to make way for Apple. Credit:Chris Hopkins

Heritage Victoria on Friday issued a refusal to Federation Square management, which had applied to knock down the Yarra Building to make way for an "Apple Global Flagship Store".