The incident took place on a bus in the capital and was recorded by a passenger before being posted online.
The group of students were verbally attacked by the woman on Sunday, when they were coming home from celebrating one of their birthdays.
Videos show the woman saying that she is a racist, and repeatedly shouting racist insults at the group.
Other passengers can be heard condemning the woman's comments, with one girl saying: "Your're disgusting" and "You're a disgrace to the country".
The Immigrant Council of Ireland tweeted about the video, calling it a "horrific incident of racism against a group of young women".
Dublin Bus confirmed the incident took place on Route 44 at approximately 7pm on Sunday evening.
They added: "All Dublin Bus drivers are trained on the comprehensive procedures for dealing with specific situations. Each vehicle is equipped with a radio which allows immediate contact to our Central Control Centre.
"This means that our drivers have immediate contact to a team of Dublin Bus Inspectors should assistance be required in any given situation.
"Dublin Bus operates a fleet of 1,000 buses and last year we carried 142 million customers. While the operation on such a large scale is challenging, the level of anti-social behaviour is relatively low.
"This is due, in part, to our commitment to embrace and foster community relations while also implementing physical mechanisms that protect our customers and employees who avail of our services.
"The entire Dublin Bus fleet is fully fitted with CCTV cameras with up to 12 cameras fitted on the more modern vehicles in the fleet. Each Dublin Bus depot has a designated staff member whose principal task is to monitor and maintain these cameras."
