Discovered during a routine operation to fix muscle problems in his arm, the disease was caught during the early stages and confirmed to be malignant.
The 30-year-old has moved back home to Budapest to be closer to his family.
Marton Fulop: "I am sure that, after a few months, I will be ready both physically and mentally, to continue playing football.
"What is more, I'd like to train between the treatment courses, as the doctors have said this is fine, and, in fact, they heartily recommend it I am very grateful for all the messages and good wishes – it really helps me that many are thinking of me.
"When training in February, I felt a sharp pain in my arm, there was bleeding and I could feel that something was pulling the tendon that moves my middle finger, and I couldn't straighten out my finger.
"I contacted Doctor Ferenc Toth, one of the country's leading hand specialists, who recognised that my hand needed immediate surgery.
"Since then, a long scar can be seen on my arm, but my hand recovered completely and I could return to playing.
"I didn't want to cover anything up as I feel I must be honest with the public and those who follow my career.
"I have thus brought my illness out into the open, the news of my operation, and soon I shall let you know about my full recovery."