Also affected were people who had changed their address or their surname after getting married.
"Police sincerely apologise to all of those who have been affected by this one-off technical issue, which has now been resolved," Mr Griffiths said.
"I can also reassure anyone who has been incorrectly ticketed as a result of our mistake that they won't need to pay the fine, and anyone who has paid in error will be completely refunded."
Police became aware of the issue when a member of the public contacted the Police Infringement Bureau (PIB) about a notice received for a vehicle she no longer owned, he said.
However, the scale of the problem only became clear this week as a result of ongoing investigations.
"Once the problem was brought to our attention, police took action to investigate and ensure it was fixed," Mr Griffiths said. "We have also put a number of steps in place to ensure it does not happen again."
The affected traffic notices included mainly speed camera infringements and a smaller number of other camera-related notices including red light camera offences, as well as police-issued parking notices.
Council-issued parking notices are not affected.
Higher demand during the busy holiday period also meant that people attempting to contact the PIB about the problem over the phone had experienced delays, Mr Griffiths said.
While the total amount of incorrectly issued notices was unknown, the individual amounts involved could potentially range from $30 to $630, he said.
"Police once again apologise to all those people affected by this problem, including previous vehicle owners as well as motor traders and dealers, who have understandably been fielding calls and complaints from concerned customers.
"If anyone has questions or concerns over an infringement they believe may have been issued incorrectly, we ask them to make contact the PIB straight away with their notice details so we can put it right," Mr Griffiths said.