The 30-year-old had only just returned after undergoing ankle surgery in May.
"Everything had been perfect in Leighton's programme and he worked extremely hard in pre-season," manager Roberto Martinez told the club website (www.evertonfc.com).
"He looked refreshed, he looked strong and he looked at a really, really good level. Then, in training, he blocks a ball and it hits him exactly in the same area where he had surgery.
"It's one of those tough moments that you have to take as a player," said Martinez.
Everton, who started the Premier League campaign with a 2-2 home draw against promoted Watford last weekend, travel to Southampton on Saturday.
(Writing by Tony Jimenez, editing by Ian Chadband)
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