The club confirmed the move in a statement released on Tuesday morning.
It said: "Newcastle United are aware of a racist remark that was directed towards Sammy Ameobi via Twitter on Sunday evening.
"The club and Sammy have reported the matter to the police, who are now dealing with the incident.
"The racist comment is wholly unacceptable. Newcastle United will not tolerate racism of any kind and will take the strongest possible action against those responsible."
The offending account has since been deleted.
Ameobi, the younger brother of Shola, appeared as a late substitute in Monday night's 3-1 Barclays Premier League victory at Stoke which saw the Magpies climb into third place in the table after a 10-game unbeaten start to the campaign.
It is not the first time a Newcastle player has found himself in the news because of the social networking site.
Former midfielder Joey Barton effectively sealed his departure from St James' Park for QPR after making critical comments about the club during the summer.
Newcastle's statement comes at a time when the Football Association are investigating claims that QPR defender Anton Ferdinand was the subject of a racial slur by Chelsea and England captain John Terry on October 23.
Northumbria Police confirmed that inquiries are under way.
A spokeswoman said: "The matter was reported to police on Sunday. Police are investigating."