The Cabinet has agreed that from Saturday passengers arriving from Britain and South Africa will need to have a negative PCR test for Covid-19.
Passengers arriving at either Irish ports or airports must have the test taken within 72 hours of travelling.
A travel ban for passengers from Britain and South Africa has also been extended until midnight 8 January.
Minister for Transport Eamon Ryan has said that a person arriving in Dublin Airport without a negative test faces a fine of €2,500 or six months in jail.
He said this measure is provisionally in place until 31 January to see how it works and what happens with the vaccine.
He said the Cabinet has provisionally agreed to apply these measures to similar Red List countries, but they will work with the EU Commission and those in the travel industry to discuss how they will broaden the measures to other jurisdictions.
The Minister said that the new travel measures are an additional protection, but are not as foolproof as testing itself.
Mr Ryan said that the measures do not avoid the risk around false positives or false negatives, but are an extra layer.
He told the press conference that the number of people travelling now is "a trickle" and down to negligible numbers.
Under the new guidelines, essential supply chain workers will be exempt from having to have evidence of a negative PCR Covid-19 test.
The Government says that an exemption over evidence of a negative PCR test can also be considered in "exceptional and urgent humanitarian cases, particularly related to an emergency medical need for the person or his/her child".
In relation to domestic travel, people must stay at home except for travel for work, education or other essential purposes. People are allowed to exercise within 5km of their home.
People are also allowed to travel outside their 5km to attend medical appointments and collect medicines, travel to attend disability day services, attend court, vital family reasons, food shopping, farming purposes, attending a wedding or a funeral, and to visit a graveyard.
Measures 'do not go far enough'
Sinn Féin's travel spokesperson Darren O'Rourke has said that the new measures "do not go far enough".
In a statement, he said the Government must require all arrivals into Irish airports and ports to require a negative pre-departure Covid-19 test, as well as mandatory testing five days after they arrive into the country.
"Our ports and airports have been a weak point in our defence against Covid-19 to date," he said. "The need to address this weakness has never been greater."
Co-leader of the Social Democrats Róisín Shortall said international travel was a weakness in the Government's response to Covid-19.
She said: "People travelling through Dublin Airport to and from Northern Ireland is another glaring weakness in the system that needs to be addressed.
"The lack of any measures to monitor UK travellers who are supposed to self-isolate after arriving here is a major concern. The Minister should also explain why just one PCR test is required."
Labour Transport spokesperson Duncan Smith said the PCR tests for arrivals from Britain and South Africa "amounts to window dressing".
He added: "If we are really serious about detecting Covid-19 then there should be testing of passengers on arrival and rigorous follow up to ensure people are quarantining until given the all clear."
Aer Lingus to require proof of test on boarding
Aer Lingus has issued a statement after the Government announcement that passengers from Britain and South Africa will require a negative PCR test to enter Ireland.
The Irish airline has said that all customers will be required to present evidence (such as an email or the text of a document) of a negative PCR test result that can subsequently be verified by Border Control staff in Ireland.
Customers that do not have such evidence will be advised that they may be prosecuted on arrival if they proceed to travel.
The airline has said customers that do not wish to travel can change their flight up to two hours before travel, on every Aer Lingus fare type.