Curtis was a surprise winner 14 years ago at Royal St. George's, capturing the claret jug in his very first appearance. He also finished inside the top 10 in both 2007 and 2008, and his withdrawal will end a streak of 14 straight Open appearances.
Curtis, 40, has made only two starts since November and has not played since withdrawing from the Valero Texas Open in April after just 10 holes, citing a shoulder injury.
Finau was added based on his world ranking and will be making his second straight Open appearance, having tied for 18th in his debut last year at Royal Troon. He has three top-5 finishes on the PGA Tour this year and narrowly missed out on qualifying for The Open last week at The Greenbrier Classic, where he finished T-7.
The Open will be played July 20-23 at Royal Birkdale Golf Club in Southport, England.