Clarke pulled out of the Nelson Mandela Invitational this week in South Africa and the Nedbank Challenge next week in Sun City, where the winner gets $2 million. He is not expected to play again until next year.
The nature of his wife's illness was not disclosed.
'Much as I am disappointed in having to withdraw from my obligations, I hope that everybody understands that it is vital I am with my wife and family at this time,'' Clarke said.
'Heather has been having problems, and we are determined to get to the bottom of them as quickly as possible.''
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