The Togo international was admitted to hospital on Saturday after feeling unwell and was diagnosed with a mild bout of the disease.
The club said the illness was detected at an early stage and Adebayor was responding well to treatment.
He is expected to be released from hospital on Monday and will then require a minimum of seven days before returning to training.
He has been advised not to travel on medical grounds and so will miss the club's pre-season tour.
- Sports & Recreation