Lancashire Police said it had issued a 42-year-old man from London with a conditional offer of a fixed penalty.
No 10 said Sunak "fully accepts this was a mistake and has apologised", adding that he would pay the fine.
BBC reports passengers caught failing to wear a seat belt when one is available can be fined £100 ($190).
This can increase to £500 ($957) 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 Sunak's Instagram account.
It is the second time 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-19 lockdown rules - by attending a birthday gathering for the then-prime minister in Downing Street in June 2020.
'Disregard for the rules'
Fixed penalty notices are a sanction for breaking the law, and mean a fine, which needs to be paid within 28 days, or contested.
If someone chooses to contest the fine, the police will then review the case and decide whether to withdraw the fine or take the matter to court.
Labour's deputy leader Angela Rayner said in a tweet that Sunak was a "total liability".
A Labour Party spokesperson added: "Hapless Rishi Sunak's levelling-up photo op has blown up in his face and turned him into a laughing stock."
The Liberal Democrats said, in becoming the second ever serving prime minister to be fined by police, he had "shown the same disregard for the rules as Boris Johnson".
Deputy Lib Dem leader Daisy Cooper said: "From partygate to seatbelt gate, these Conservative politicians are just taking the British people for fools.
"Whilst they continue to behave as though it's one rule for them and another for everyone else, this fine is a reminder that the Conservatives eventually get their comeuppance."
But earlier Conservative MP for Blackpool South Scott Benton suggested Lancashire Police were wasting their time by looking into the incident.
"The vast majority of people would think that politically motivated complaints about a seatbelt are not good use of frontline resources," he said.
Passengers aged 14 and over are responsible for ensuring they wear a seat belt in cars, vans and other goods vehicles if one is fitted. Drivers are responsible for passengers under 14.
Exemptions include having a doctor's certificate for a medical reason, or being in a vehicle used for a police, fire or other rescue service.