People are required to stay at home except for exercise or other essential purposes.
Over 400 fines have been issued by An Garda Síochána for non-essential travel since Monday, 11 January.
Gardaí said the vast majority of the fines, over 300, were issued this weekend for suspected breaches of the public health regulations relating to non-essential travel.
As of Friday evening, 74 fines for non-essential travel had been processed.
In a statement on Monday, An Garda Síochána said the fines issued over the weekend will now be checked and processed, with a definitive figure available when this process is complete.
Ahead of the weekend, Gardaí said the public need to plan their activities this weekend to take into account that people are only allowed to exercise within 5km of their home. You cannot travel more than 5km to a location to exercise.
While the vast majority of the public have been complying with the restrictions, however, a minority were breaching them.
Gardaí at a checkpoint in Ballymahon in Longford over the weekend said more than 70 drivers were asked to turn around and go home.
People were also advised to avoid public amenities if they are crowded, while parking illegally at said amenities runs the risk of vehicles being towed and impounded.