The footage shows the officer approaching the car in the Palestinian refugee camp Qalandia and shouting at those inside.
After a brief exchange, he throws the stun grenade through the open door and forces it closed as the driver tries to escape. There is a blast and smoke is visible.
The two passengers escape from the other side before the officer appears to fire his rifle as they duck for cover. Israeli rights group B'Tselem said everyone in the car survived.
Police told Israeli media the officer had not acted "in accordance with procedure".
It said the incident had been transferred to the department of internal police investigations.
In a separate incident in Qalandia on Sunday, Israeli forces shot and killed a 16-year-old boy, Walid Abu Sneineh, according to the Palestinian health ministry.
Two other children suffered gunshot wounds to their lower limbs, it added.
Israeli authorities told the BBC that Israeli forces perceived an imminent threat to their lives after "a violent riot erupted during which [they] came under a massive barrage of stones".
They said the forces responded with gunfire to "a suspect throwing stones at them from a rooftop".
Also on Sunday, a critically ill four-month-old baby, Ahmed Zaid, died after Israeli troops refused to open a gate blocking the main entrance to his village west of Ramallah, delaying his access to urgent medical care, according to the head of the local UN human rights office.
Ajith Sunghay said an ambulance was waiting on the other side of the gate outside Deir Ammar to take Ahmed to hospital.
He described the death as "senseless" and "emblematic of an occupying power continuing to show utter disregard for the humanity and rights of Palestinians living under occupation".
However, the Israeli military told the BBC that its troops "allowed the baby and his family to pass without any delay to continue receiving medical treatment".