The England international has missed Chelsea's past two league games - a 3-0 defeat by Brentford and a 5-1 win over Bournemouth.
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"The 26-year-old was absent from Saturday's 5-1 victory over Bournemouth at Stamford Bridge while medical assessments took place following the injury suffered in training," the club said in a statement.
"Those assessments confirmed surgery would be the required course of action.
"Reece has already begun his road to recovery and will be supported by the club's medical department at Cobham during this rehabilitation phase."
Chelsea are sixth in the Premier League ahead of Saturday's visit to Everton.