'I made up my mind several weeks ago to play until after my favorite tournament, the Open, and then that would be it for a while,' Clarke said Saturday on his Web site.
Clarke was in the hunt after opening with a 3-under 69 at Royal Liverpool, then followed with an 82 -- his worst score in the British Open -- to miss the cut for the first time since 1998.
Heather Clarke was diagnosed with breast cancer, which returned last year and has spread throughout her body. Clarke has tried to keep playing and finished third at the Bay Hill Invitational, but he has withdrawn from tournaments when his wife's health worsens.
'My game has been good, but my mind has obviously been elsewhere,' said Clarke, who has two young children. 'Now the priority is to be with my wife and family and support them in every way that I can.'
Clarke is 26th in the Ryder Cup standings for Europe; the top 10 qualify, and captain Ian Woosnam is allowed two picks. He has played in every Ryder Cup since 1997, compiling a 7-7-3 record.
'I know that many people will be wondering about the Ryder Cup, but such things are not in my thoughts at the moment,' Clarke said. 'Now is the time to concentrate on matters much more important than golf.'
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