The club's officials contacted Northumbria Police after the 30-year-old was alleged to have been targeted on the social networking site Facebook.
The comments have since been deleted.
A Magpies spokeswoman said the club would always take action against people racially abusing club players.
She said: "We have liaised with Northumbria Police and the matter is now in their hands.
"We have a zero-tolerance approach to racism and will always seek to take the strongest possible action."
A Northumbria Police spokesman said: "We have received a report of racist comments made on Facebook, on which we're working closely with Newcastle United.
"Northumbria Police take all reports of racist abuse very seriously and inquiries are being conducted."
Ameobi, of Jesmond, is Newcastle's longest-serving player.
The forward, who was born in Zaria, Nigeria, made his first team debut in a home game against Chelsea in September 2000.