The incident occurred over two weeks ago.
A Garda spokesman at Henry St said: “It is being investigated by a community policing unit.”
It is alleged the group got the dog to run out in front of a passing van, by having it chase after a ball.
The University of Limerick said action, including expulsion, would be taken if students were involved.
The incident came to light in a letter to the local media from Charlie Cassey, of College Court Drive, Castletroy, who said the incident sickened her.
She stated: “As the students finish their exams the giddiness grows and the parties begin. I don’t begrudge them this, but this method of entertainment is unforgivable. As they gathered by the green, a small dog from the neighbourhood was drawn by the small, excited crowd. As cars drove up and down the road at a fast pace, the students teased the dog by throwing the ball from one side of the road to the other — the dog of course chasing the ball.”
Her brother-in-law also witnessed the incident.
Ms Casey stated: “The students actually waited until a van was coming before playing this sick game until the inevitable happened — the little dog went under the wheels of the van.
“Did the students feel remorse? No. As the dog lay dying in agony, the students laughed and jeered at my brother-in-law as he roared and scolded them.”
In a statement, UL said it encouraged any individual who is affected by antisocial activity in the area to report it to gardaí, and where student involvement is suspected, to alert the college.
A UL spokeswoman said: “Where it transpires that the individual(s) are students of the university, they are subject to the discipline process where the penalties on conviction range from fines, suspension, and in serious cases may involve dismissal from the university.”
Adam Moursy, UL Students Union president, said what was alleged to have occurred was an unfair representation of the vast majority of students.