The former Santos player has been put on a special diet by the club after signs of the condition were detected just days following his arrival at the Catalan club.
Anaemia affects the number of haemoglobin in blood cells, which can lead to a shortness of breath and tiredness.
Spanish newspaper El Pais quotes an unnamed source as saying that Neymar is being monitored by the club.
"Neymar is being treated by Barcelona's doctors for signs of anaemia with an adequate diet and complementary course of vitamins," he said.
Neymar made his debut as a substitute in Barcelona's 2-2 draw with Polish side Lechia Gdansk and also featured from the bench in the 8-0 humbling of his former side Santos.