Police said a grey Fiat Punto and grey Mazda 2 had collided at around 10.40pm last night (Friday).
It happened at the junction of Wiggan Lane and New House Road in the Deighton area of the town.
The driver of the Fiat, a 56-year-old man, was taken to Leeds General Infirmary for treatment for potentially life-threatening injuries.
He remains in a critical but stable condition, police said today.
The driver of the Mazda, a 25-year-old woman, was taken to Huddersfield Royal Infirmary with minor injuries, as was a male child who was a rear-seat passenger in the car.
A girl, who was also a rear-seat passenger, was uninjured.
A third vehicle, which was parked and empty at the time, was also damaged during the collision.
Appealing for witnesses, a West Yorkshire Police spokeswoman said: "Two people are believed to have assisted in the immediate aftermath of the collision.
"Police would like to trace these people and ask them to come forward, along with anyone else who may have been in the area and seen either vehicle travelling before the incident, or anyone who witnessed the collision itself."
Information can be passed to officers at the Safer Roads and Neighbourhoods Support Team West by calling 101 and quoting 13170597775.