SEOUL (Reuters) - Park In-bee's chances of playing at the Rio Olympics golf tournament dimmed further on Tuesday after the South Korean world number three pulled out of an international team event due to a lingering thumb problem.

The seven-times major champion, who was inducted into the LPGA's Hall of Fame earlier this month, has been plagued by injury this season and is without a victory in 10 starts.

She has missed two cuts, withdrawn after the first round in three events, and posted her worst ever score as a professional, 12-over-par 84, in the first round of the LPGA Volvik Championship in May.

Her management company said on Tuesday she would skip the July 22-24 International Crown event, which pits eight countries against each other at Merit Club, Illinois.

"Park In-bee notified the LPGA that she will be unable to attend the International Crown due to her left thumb injury," her management company, Galaxia SM, told Reuters.

The 27-year-old, who has raked in almost $13 million in career earnings on the LPGA Tour, said before the Women's PGA Championship this month that she would not go to Rio if she was not fully recovered from the injury.

"At the Olympics, you play for your country, not for individual honor. If I'm not in top condition, I'd rather give the opportunity to another player," she said.

Park missed the cut at the event, carding an 8-over 79 in the second round.

The top 15 players in the world rankings as of July 11 qualify automatically for the Rio Games, where golf is making its return to the Olympic program after a 112-year absence. Each country can send a maximum of four players.

Currently, Kim Sei-young, Chun In-gee and Amy Young make up the other three places, but there are five more South Koreans in the top 20 battling for Olympic spots.

(Writing by Peter Rutherford; Reporting by Jee Heun Kahng; Editing by John O'Brien)