Milan said doctors expected Gazidis to "make a full recovery" and that he will continue working in his role as he undergoes treatment.
"AC Milan informs its fans and stakeholders that our CEO, Ivan Gazidis, has been diagnosed with a cancer of the throat," a club statement read. "Based on an extensive series of tests and scans, doctors expect he will make a full recovery.
"Ivan will remain operational during the necessary treatment in specialised clinics, with the full support of the ownership, President Scaroni and the club's senior management.
"Everyone involved with the Club wishes Ivan all the best for a full and speedy recovery. We are all with you."
Gazidis, who left Arsenal to join Milan in September 2018, remained positive about the diagnosis.
"Of course, there is never a good time for a diagnosis of cancer," he said. "But I have a very curable form of cancer and a positive diagnosis.
"I have world class medical expertise, and the support of so many loved ones and everyone at the club, and I am confident based on all advice that the cancer will be treated successfully, with a full recovery.
"My diagnosis demonstrates the importance of regular medical check ups, even if you don't have symptoms. I would encourage everyone to prioritise their health and to make sure, even in the day to day obligations of life and work, that they have their regular medical checkups.
"We have a strong team, both on and off the pitch and I have full faith in their ability to drive our club forward over the coming weeks. See you soon and always Forza Milan."