People can now be issued a fine of up to €100 for breaching the 5km travel limit.
The fixed charge penalty notice will arrive in the post and a person will have 28 days to pay it.
Gardaí say it'll also no longer consult with the Director of Public Prosecutions before issuing these fines.
They will continue to engage, explain, encourage before handing out the fine as a last resort.
For the rest of the month people are being asked to stay at home, except for travel for work, education or other essential purposes, or to exercise within 5km of their home.
Deputy Garda Commissioner John Twomey, Policing and Security said, "An Garda Síochána continues to see significant compliance by the public with Public Health Regulations, however we also continue to see some activity which is in contravention of these regulations introduced to stop the current spread of Covid-19 and protect our communities. I appeal to every person without a reasonable excuse for travel - Stay at Home, this is your duty as a citizen and will save lives and support our front line services, nurses, doctors, hospital staff and my Garda colleagues at this time.”