A massive 300% increase in the offence - which can attract a fine of up to £1000 - has been recorded since Police Scotland came into being last year.
Scottish Liberal Democrat leader Willie Rennie said the practice was "unfair and unreasonable".
The Sunday Herald recently revealed allegations that Police Scotland's target culture was affecting the behaviour of officers.
Former officers said bogus stop and searches were being entered into the computerised system to boost the overall figures. Police Scotland said more than 500,000 searches were recorded in the first nine months of the new force.
Road safety and reducing road crime is a key priority, but insiders have also expressed concern about what they believe is unfair targeting of motorists.
Under road traffic legislation, it is an offence for a driver to have a licence with incorrect details such as their address.
Two sources said that drivers in new estates, who were likely to have moved house but not updated their licence, were being stopped by officers.
On this basis, the Sunday Herald asked how many of these offences had been recorded over two identical periods. Between April and December 2012 - the final year of the eight old territorial forces - 408 offences of failing to correct the address on a licence were recorded.
For the first nine months of the single force, the number had surged to 1645 - a jump of over 300%.
Officers can stop a driver and ask to see his licence without suspecting that an offence has been committed. Getting caught with an outdated address can result in either a warning or a report being sent to the procurator fiscal.
The maximum penalty that can be imposed by the courts is £1000. The huge rise comes against a backdrop of Police Scotland taking firm action against road traffic breaches. In the nine-month period for 2012, the old forces recorded 192,750 motoring offences.
The figure for Police Scotland between April and December was 230,956 - a near 20% rise.
The old forces recorded 23,049 mobile-phone offences in the same period, but there was another surge of around 20% after the single force was introduced.
The Sunday Herald's sister newspaper, The Herald, was last year leaked the Police Scotland key performance indicators in areas including speeding and mobile phone offences.
The single force has always denied setting targets for individual officers.
Richard Freeman, a solicitor advocate who has around 20 years experience in dealing with road traffic cases, said failing to update an address was a "trivial" offence.
Freeman added: "I've seen more of these cases in the last six months than in the last 15 years. In previous years, discretion would be used, but the fact that there are targets means common sense isn't being exercised."
He also said: "I can tell you that police officers have quotas to reach on road traffic offences. I've cross-examined them in court."
Michael Lyon, another solicitor who specialises in motoring issues, said: "This is about boosting the figures for the prosecution of a relatively minor offence. It's like shooting fish in a barrel. There are many more serious and arduous offences that the police could be detecting."
Scottish Liberal Democrat leader Willie Rennie said: "Targeting drivers who have just endured moving to a new house and have not had sufficient time to correct all their official documentation is unfair and unreasonable. This kind of unthinking policing risks creating distrust between the police and the communities they seek to protect. The Chief Constable should investigate this matter urgently."
Chief Inspector Simon Bradshaw, of the Road Policing Unit at Police Scotland, said: "Road safety is one of the top priorities set by local communities to keep people safe. People consistently tell us that road safety issues concern them.
"Since the creation of Police Scotland and because of this priority set by local people there has been increased activity and enforcement of road traffic offences.
"Police Scotland has not and does not target drivers living on new housing estates. There are no targets, and there have never been, for road policing officers in Police Scotland. We seek to influence road-user behaviour and work to keep people safe."