The 21-year-old joined Barcelona this summer for a fee said to be around £48.5m but has been starting off the bench for the La Liga champions in pre-season action.
Now he may miss Barcelona's tour of Thailand to undergo treatment for the blood disorder. He is currently on tour with the club in the West Bank and Israel.
Anaemia derives its name from Ancient Greek and literally means 'lack of blood.'
It arises when there is a lack of red blood cells or when there is less than the normal amount of haemoglobin in the blood.
Anaemia can lead to people feeling tired or weak and can also cause shortness of breath, dizziness, and headaches.
Barcelona have put Neymar on a special training programme to help him combat the condition.
Neymar has had minor health issue already this summer. Just last month he successfully underwent surgery to remove his tonsils and clear a nasal passage.