The Togo international, 30, was sent to the hospital after being diagnosed with a mild case of the virus and will now miss the club's preseason tour of the United States.
"[Adebayor] was admitted to hospital on Saturday after reporting feeling unwell to our medical staff," a Tottenham statement read. "A swift diagnosis meant the disease was detected at an early stage and he is responding well to treatment. The striker is expected to be released from hospital [on Monday] and will then require a minimum of seven days before returning to training.
"The player has been advised not to travel on medical grounds, which means he will be forced to miss our preseason tour of North America."
Tottenham has three friendlies against MLS sides in the space of seven days, beginning with a clash against the Seattle Sounders on Saturday.
Along with coming up against onetime player and current Sounder Clint Dempsey, Tottenham will also meet former hero Jermain Defoe when it travels to Toronto FC.
The club's final friendly of the tour will see Tottenham face the Chicago Fire on July 26.