The principal of the nearby boys' school texted all mums, dads and guardians of students to ensure that all are aware of safety procedures.
It is understood that a young girl was stopped by a middle-aged man with grey hair.
She immediately informed her parents, who told the school.
"A girl from the senior girls school was approached today at 2.25pm by a grey-haired middle- aged man," the school sent in a text. "Please advise of safety procedures." Local councillor Jane Horgan-Jones said residents are particularly cautious this week.
"It is very concerning," she told the Herald.
"I heard anecdotally that parents and guardians got a text from the school.
"It is probably just a precaution that the school are taking at this stage.
"It is important that all children are aware of the dangers and the school and teachers are telling children not to speak to strange adults.
"Certainly, if all the parents are aware, the community will step up vigilance," she added.
Gerry Breen, of Fine Gael, whose children attended the school several years ago, said that there is always a strong community spirit in Clontarf.
"Residents will be particularly alert now," he added.
The news comes after reports of a man in Limerick who approached school children in the area just before Christmas.
And in a separate incident, a garda intercepted a stranger who was "walking" a teenage boy home from school.
Gardai investigated the incident after it was noticed that the middle-aged man was carrying one of the boy's schoolbags.
The man, when questioned by the garda, said that he had been friends with the boy for a number of months and sometimes walked with him on his way home from school.
He discovered the man had engaged in inappropriate conversation with the boy.