The Togo international, 30, was hospitalised after being diagnosed with a mild case of the virus.
The Premier League outfit confirmed Adebayor will remain in England while his team-mates prepare for the 2014-15 season.
"The Togo international 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 tomorrow 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 pre-season tour of North America."
Tottenham have three friendlies against MLS sides in the space of seven days, beginning versus the Seattle Sounders on Saturday.
Along with coming up against former player and current Sounder Clint Dempsey, Tottenham will also meet former hero Jermain Defoe when they travel to Toronto FC.
Their final friendly of the tour will see them tackle the Chicago Fire on July 26.
