Strauss's wife Ruth was diagnosed in December and is entering a new period of more demanding treatment.
Speaking in a video on the England and Wales Cricket Board's Twitter account, Strauss said he would be temporarily replaced by former England coach Andy Flower.
"He will keep a very steady hand on the tiller while I am away," Strauss said. "I need to step back and look after my wife and the family for a period of time."
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England face Pakistan at Lord's on Thursday in the first test of the summer.
(Reporting by Martyn Herman; Editing by Toby Davis)
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