Adebayor was admitted to hospital on Saturday after feeling unwell, the club's website (www.tottenhamhotspur.com) reported.
"A swift diagnosis meant the disease was detected at an early stage and he is responding well to treatment," the club said.
"The striker is expected to be released from hospital tomorrow and will then require a minimum of seven days before returning to training."
Adebayor, who scored 14 goals for Tottenham last season, will miss the club's pre-season tour of North America.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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