The government announced last week that it would now require arrivals to complete a "passenger locator form," which has been voluntary since the quarantine rule was introduced last month.
Britain will introduce similar quarantine measures from June 8 and also announced the details on Friday. Those measures will not apply to people arriving from Ireland.
Airlines have told both governments that the rules are impossible to implement.
The Irish regulations will apply to all nationalities, including returning Irish residents, and be reviewed on June 18. Harris told Reuters this week the government "honestly don't know" how long they will be needed.
Failure to complete the form or to update contact details if they change, or providing false information, could lead to a fine of up to 2,500 euros ($2,700) or six months in prison.
Aircraft crew, hauliers and passengers transiting to another jurisdiction will be exempt.
"These are extraordinary measures but they are necessary in a time of a public health crisis," Harris said in a statement.
The number of confirmed coronavirus cases in Ireland rose by 115 to 24,506 on Friday, with related deaths up 11 to 1,592.
It was the first time in seven days that the number of new cases had exceeded 100.
Ireland's Chief Medical Officer, Tony Holohan, said the cases stemmed from exposures prior to the easing of stay-at-home restrictions a week ago.