Lancashire Police said it had issued a 42-year-old man in London with a conditional offer of a fixed penalty.
Mr Sunak had previously apologised for the incident, saying it was an “error of judgement”.
Passengers caught failing to wear a seat belt when one is available can be given an on-the-spot fine of £100.
This can increase to £500 if the case goes to court.
The prime minister was in Lancashire when the video was filmed, during a trip across the north of England.
The video – to promote the government’s latest round of “levelling up” spending – was posted on Mr Sunak’s Instagram account.
It is the second time Mr Sunak has received a fixed penalty notice while in government.
Last April, he was fined along with Boris Johnson and wife Carrie for breaking Covid lockdown rules – by attending a birthday gathering for the then-prime minister in Downing Street in June 2020.