Murray said he was tired, while Williams claimed she was suffering with an elbow injury.
"I practiced 40 minutes and felt pretty exhausted," Murray told a news conference ahead of his match against Belgian David Goffin.
"It didn't make sense for me to keep going because when you feel like this it becomes a risk to play."
Murray recently won back-to-back tournaments in Munich and Madrid, the first claycourt titles of his career.
"They've been three very long weeks for me," Murray added. "The longest on clay in my career."
Williams, who has won the tournament for the last two years, cited a right elbow injury as the reason for her withdrawal.
"I've been dealing with it since last week in Madrid," Williams, who was due to play Christina McHale, told a news conference.
"It was a difficult decision but I should be ready for Paris."
Both players will now rest in preparation for the French Open, which starts on May 24.
(Reporting Jacopo Lo Monaco; Editing by Toby Davis)
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