MIAMI—General Growth Properties Inc. and Ashkenazy Acquisition Corp. are paying $280 million for a 20% stake in the company that owns much of this city’s Design District, betting on the emerging luxury-retail neighborhood as some 50 brands prepare to open new stores.

The deal with Miami Design District Associates, announced Tuesday, comes at a time when malls are growing slowly and luxury shops on busy urban streets like Fifth Avenue in Manhattan or Michigan Avenue in Chicago—sometimes called “high street” retail—remain bright...