Angela Ahrendts, the former Burberry chief hired by Apple five years ago to oversee its stores, said Tuesday that she would leave the company in April.

The departure is an unusual move for a top executive at Apple, which is facing retail challenges as sales in China have dropped and iPhone sales have turned sluggish.

Ms. Ahrendts, 58, was one of Apple’s most prominent hires when the Silicon Valley company lured her from Burberry with an initial $73 million pay package in 2014. She had spent eight years as Burberry’s chief executive and was credited with expanding it into an international fashion brand.

Over five years, Ms. Ahrendts was among Apple’s highest-paid executives, earning more than $170 million, according to securities filings.