Mabbutt, 51, won the UEFA Cup and FA Cup during his time at White Hart Lane and is a firm favourite among Spurs supporters.
"The club are delighted to report that Gary Mabbutt is now making a successful recovery from an emergency operation to cure a circulation blockage in his left leg," a statement on Tottenham's official website read.
"Our former captain was admitted to Kings College Hospital, London, for a peripheral artery bypass operation and will remain in hospital for a two-week recovery period.
"Everybody at the club would like to wish him a full and speedy recovery, while Gary himself would like to thank his dedicated medical team and staff at Kings College."
Former Spurs team-mate Gary Lineker added on Twitter: "Gary Mabbutt has had emergency surgery. Don't know details, but I do know there is no man more gutsy than Mabbs. Get well soon."
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