Ireland's stable environment could help attract further foreign investment, especially from firms who are looking to access the European markets, according to Fitzgerald.
"There is legal certainty, [and] a government that's very pro-business, pro-enterprise," she said.
The minister said that Dublin remained committed to its relatively low corporate tax rate of 12.5 percent. Globally, corporate taxes measure at about 22.5 percent on average, according to the Tax Foundation, a U.S.-based independent tax policy non-profit. Europe has the world's lowest corporate tax rates at about 18.9 percent on average, according to the non-profit.
Ireland will also be "a strong voice" against any proposals to raise taxes within the EU, one of which was a possible move against big U.S. tech companies such as Google,Facebook and Airbnb, Fitzgerald added.
"Some of those proposals require unanimity, and we certainly won't be supporting that," she said.
However, not everyone has been positive about Ireland's outlook post-Brexit.
In the financial space, for example, London's position as a leading hub may not see the significant decline that some are expecting, said Tony Nash, chief economist at advisory firm Complete Intelligence. That means it's unlikely Ireland will take up the mantle in the sector, Nash added.
"You definitely will get some marginal activities in Ireland, but I don't believe you're going to see large scale activities move to Ireland because the infrastructure around financial services is delicate, and it takes a long time to build up," he said.
Another concern is the potential creation of a hard trade border between the Republic of Ireland, which is an EU member, and U.K.-ruled Northern Ireland post-Brexit.
Currently, people and goods move between the two seamlessly. Ireland also exports 40 percent of its goods and 20 percent of its services to the U.K., twice the EU's average.