Kyogo Furuhashi joined Celtic this summer
The club said it had carried out an investigation and identified the individuals involved.
It has also banned the supporters’ club which they belonged to from receiving tickets for future fixtures.
The social media footage emerged on Sunday when Rangers were in Dingwall to play Ross County.
Police Scotland said it was aware of the video and that “officers are liaising with the club to make relevant enquiries”.
The footage appeared to have been filmed on a supporters’ bus.
‘Not representative of our club’
After it came to light, Rangers said it was investigating to identify the individuals involved.
“Rangers condemns all forms of racism and discrimination,” it added.
“Those who partake in such behaviour are not representative of our club or the loyal support who have stood by us through thick and thin.”
In a statement released later on Monday, the club said: “The individuals involved have been identified and will be banned indefinitely from all Rangers games.
“Furthermore, the RSC of which they were members and travelled with to the game, have been banned from receiving tickets for future fixtures.”
Since joining from Japanese side Vissel Kobe this summer, 26-year-old Furuhashi has scored six goals in seven games and become an immediate favourite among Celtic fans.
After the footage came to light, Celtic tweeted: “If reports are accurate then such sickening and pathetic racist behaviour directed towards Kyogo Furuhashi deserves absolute condemnation.
“Unfortunately, a number of Celtic players in recent years have suffered similar racist abuse.
“As a club open to all, we stand firmly against racism in all its forms and we will give Kyogo our full support. All stakeholders must work together in tackling all forms of bigotry.”
Manager Ange Postecoglou told Celtic TV that he was saddened.
“Our number one priority is to protect and support the player. He’s a cracking guy,” he said.
“If anyone ever comes across him, he’s such a nice young man and he doesn’t deserve any of that type of behaviour – no-one does.”
Furuhashi himself tweeted: “I’ll never walk alone.”
Celtic face Rangers at Ibrox next Sunday in the opening Old Firm derby of the Scottish Premiership season.