Jim Taylor, headteacher at St John Fisher Catholic Voluntary Academy on Oxford Road, sent out a letter today (March 15), encouraging parents and pupils to be wary of stranger danger.
Three teenagers witnessed the man on Staincliffe Hall Road as they walked home from school on Wednesday. Scared, they ran for cover.
Mr Taylor's letter to parents said: "In the incident, a car stopped by the side of the road near to a group of students from the school.
"One of the occupants got out of the car and our students have reported that he was holding a knife.
"The students immediately ran off to a place of safety and police are investigating."
A West Yorkshire Police spokesperson said: "Police were contacted at about 3.48pm on Wednesday by a resident reporting that three school children had witnessed a man holding a knife on Staincliffe Hall Road, Dewsbury.
"The male got into a car with other persons and drove off before then driving back past the three females, heading towards Heckmondwike. The girls then went into a shop to speak with an adult about what they had seen."
Enquiries are ongoing and anyone who saw what happened is asked to contact Kirklees Police on 101 referencing crime number 13190132850.