Patrick Moratoglou, speaking to the New York Times, said the pectoral injury that prompted her to withdraw during the French Open was "muscular" and would "probably have become a tear" if she had kept playing the tournament.
"So in 15 days, it should normally be healed, and she will be able to play again," he said.
Williams will take a break and then start training again at Moratoglou's academy, he added. She plans to arrive in Britain a week before Wimbledon.
WATCH—Patrick Moratoglou discusses Serena's injury after her withdrawal:
The three-time French Open champion had reached the fourth round of the tournament in singles but withdrew from her scheduled meeting with Maria Sharapova, and had appeared to be hampered during her doubles match the previous day.
Williams, who has played just three singles events since returning from the birth of her first child, will now be in the world's Top 200 in the rankings. She will use a protected ranking for Wimbledon.
Tournament organizers have not announced whether they will give her a special seeding.
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