Kim is third in the current United States Ryder Cup table
American world number 11 Anthony Kim and former US PGA champion David Toms have both pulled out of next week's Open Championship at St Andrews.
Kim, who finished third at the Masters in April, has not played since the start of May when he went in for surgery on a thumb injury.
Toms has played the last four weeks in the United States but has been battling with a shoulder injury for a while.
Their places will be taken by fellow Americans Ricky Barnes and Davis Love.
Barnes and Love failed to book a place at the Open after missing out at the qualifying event in Texas in May but at 64th and 68th in the world, they are the highest non-exempt players in the rankings.
Love, 46, will now extend his run of playing in every Open since he made his debut in 1987.
The withdrawals mean that England's Brian Davis is now second reserve for the tournament.
Kim went in for surgery nine weeks ago and was told then that he could expect to be out of action for 10 to 12 weeks.
He has played with the knowledge that he had a torn cartilage and said: "Compensating for it was starting to cause other issues, including a sore shoulder."
Earlier this week it was announced that Alejandro Canizares, the son of former Ryder Cup star Jose Maria Canizares, has earned a place at the Open courtesy of his runner-up spot at the French Open.
The 27-year-old was one of six additions to the line-up for the 150th Open confirmed by organisers the R&A on Monday.
The others are Justin Rose - whose AT&T win in Pennsylvania secured his place - and Americans Jeff Overton, Ryan Moore, Rickie Fowler and Bubba Watson.
Canizares, whose father played for Europe in four Ryder Cups, will be making his Open debut.
Fowler and Overton booked their places courtesy of their positions as the highest-ranked players, not already exempt, in the world rankings.
Fowler, ranked 37th, is set for his Open debut, while Overton (63rd) will be making a third consecutive appearance. He finished joint 13th at Turnberry last year.
Watson secured his second Open appearance by finishing as the second player, not already exempt, on the PGA Tour mini money-list.
One Open place has been reserved for the leading player, not already exempt, finishing in the top five at each of the Barclays Scottish Open and the John Deere Classic this week.