The federation on Thursday described the remarks as "unacceptable and racist."
Giannis Antetokounmpo, an 18-year-old Greek shooting guard and the Athens-born son of Nigerian immigrants, was selected by the Milwaukee Bucks. He was received this week in Athens by conservative Prime Minister Antonis Samaras.
Leader of the far-right Golden Dawn party, Nikolaos Michaloliakos, likened the 2.06-meter (6-foot-9) player to a "chimpanzee" in a television interview on Tuesday.
Antetokounmpo was selected in 15th place in this year's 60-player NBA draft, announced in New York on June 27. He was seen celebrating the news at the Barclays Center in Brooklyn, crossing himself in the Orthodox Christian fashion, waving a Greek flag, and hugging family members who were also present.
Golden Dawn has seen a recent surge in support as Greece endures a sixth year of recession, mounting an aggressive campaign against illegal immigration and the austerity measures imposed under the country's bailout program.
In elections last year, the party won 18 seats in the 300-member parliament, and is currently the third-strongest in opinion polls which suggest its popularity has increased further to about 10 per cent.
Prime Minister Samaras has frequently described Golden Dawn as "neo-Nazis" — a label which the party rejects, though leading members of Golden Dawn have in the past openly expressed admiration for Nazi leader Adolf Hitler and denied that the Holocaust occurred.
Samaras said he felt "great emotion" at his meeting this week with the towering teenager and his parents.
"I thank you for honouring our national colours," he said. "I hope you drive them crazy with your slam-dunks ... All of Greece is so excited for you."