The victim and his girlfriend were crossing the road near Emibois at around 1am on Saturday morning to reach a bus stop on the other side of the road, Jura cantonal police said in a statement.
Whilst on the pedestrian crossing, the man was hit by a car travelling in the direction of Noirmont.
Although a doctor arrived at the scene quickly afterwards, followed by an ambulance, the 21-year-old man died at the scene from his injuries, said police.
His girlfriend, slightly injured and in a state of shock, was taken to hospital in Delemont.
After hitting the man, the 26-year-old driver of the car continued driving along the road, colliding with two road signs before heading back to his home in the area.
He has now been questioned by police.