Shares of Oracle, which is based in Redwood Shores, Calif., declined about 2 percent in after-hours trading.

Word of Mr. Hurd’s leaves came the week before Oracle’s big annual conference in San Francisco.

“Though we all worked hard together to close the first quarter, I’ve decided that I need to spend time focused on my health,” Mr. Hurd, 62, said in a message to employees. “At my request, the board of directors has granted me a medical leave of absence.”

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Ms. Catz told analysts in a conference call that she and Mr. Ellison should have no trouble handling Mr. Hurd’s responsibilities during his leave.

“He needs to focus on his health and taking care of himself,” she said.

Mr. Hurd, considered one of the most capable managers in the technology industry, spent 25 years at the business-technology company NCR before moving to Silicon Valley to become chief executive of Hewlett-Packard. He led HP for five years before he was ousted in 2010 after a high-profile scandal over his relationship with a consultant to the company.

Mr. Hurd was swiftly hired by Oracle, which competes with his old company and has fought legal battles with other software companies and Google. Lately, he has been particularly involved in Oracle’s response to the shift to cloud-based subscription offerings.