The drivers have invalid temporary permits because they failed to complete the training they are obliged to follow after passing a practical test, the SonntagsZeitung newspaper said.
The paper cited statistics from the federal highways office that showed 7,991 new drivers had failed to follow the two mandatory courses within three years of passing their test.
Such motorists risk a stiff fine amounting to their pay for 180 days and face having to recommence the process of obtaining their licence from square one,
In case of accidents, such drivers are also uninsured, the newspaper said.
In 2005, Switzerland introduced a two-phased driving permit system.
The system requires candidates who pass their driving test to follow two courses within three years to fully validate their probationary licence.
The highways office said in most cases the fault lay with motorists for not taking the courses.
But the Tribune de Genève said a great number of drivers simply forget to renew their temporary licences.
A proposal has been made in the lower house of parliament to make the training courses optional but this has yet to be approved by the senate or the highways office.
The office does not issue reminders to temporary licence-holders when their term for completing the4 courses closes, leaving that responsibility to the motorists.