Ms Ahrendts joined the iPhone-maker last week from luxury clothing firm Burberry.
This week's stock award coincided with Apple's share price hitting $600 for the first time since the end of October 2012.
The Indiana-born executive has been granted a maximum of 113,334 restricted stock options, which will transfer to her in a series of payments starting over the next four years.
Around 85% of the shares will be awarded to Ms Ahrendts based on how long she stays with Apple regardless of performance. The remainder will be based on the stock price of the firm.