The teacher, Sarabjit Kaur, 35, had just arrived on duty at 7.45am and was parking her scooter outside the school boundary when an unidentified man fired three shots at her, killing her on the spot.
Her daughter ran away in panic.
Police said Sarbjit was divorced in 2012 and stayed with her daughter in a rented apartment at SBP Society, about 2 km from the school in Kharar.
An eyewitness, Inderjit Singh, said a man wearing a shawl had been roaming outside the school since morning.
Sarabjit was rushed to a nearby private hospital in Phase 6, Mohali, where she was declared brought dead.
The body has been kept at the civil hospital mortuary where her father, who stays in Phase 4, Mohali, also arrived.
The school authorities declared a holiday for the day.
Sarabjit taught French and Punjabi at the school since this April.
Prasanta Patnaik