LaChapelle, who has photographed celebrities for magazines such as Vanity Fair and Rolling Stone, is suing for unspecified damages.
His case states “the music video is directly derived from and substantially similar to the LaChapelle works”.
A spokeswoman for Rihanna, 22, was not immediately available for comment.
The video for S&M has been banned in some countries due to its sexual content.
LaChappelle said Rihanna has appropriated eight of his images into the video, including one where she is shown in profile against a blue background with a sweet on her tongue.
The case states that Rihanna’s video copied the “composition, total concept, feel, tone, mood, theme, colours, props, settings, decors wardrobe and lighting” of his work.
Rihanna won the best dance recording Grammy award on Sunday for her track, Only Girl (In the World).
LaChappelle is one of the fashion industry’s most respected fashion photographers.
His subjects include Lady Gaga, Kanye West, Chris Rock, Madonna and Naomi Campbell.
He has also directed music videos and stage shows.
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