The Department of Foreign Affairs is attempting to find them safe passage from the country.
Minister for Foreign Affairs Simon Coveney has said that there are 15 Irish nationals attempting to flee Afghanistan after the Taliban took control of the country.
Speaking on RTÉ's Morning Ireland on Monday morning, Coveney said there are currently 23 Irish nationals in Afghanistan and 15 of them want to leave the country.
The Department of Foreign Affairs is currently working with EU countries, the US and the UK to find routes out of the country for the Irish nationals.
"We think there are 23 Irish nationals and we have been in contact with all of them either directly or through the organisations that they work with," Coveney said.
"Many of them work with NGOs like MSF (Médecins Sans Frontières) or WFP (World Food Programme).
"Fifteen of them have told us that they want to leave and we’re coordinating that through the embassy in Abu Dhabi because we don’t have an embassy in Kabul and of course we’ll stay in very close contact with those nationals."
He added: "Most of them would have been booked on commercial flights out of Kabul, that is work that has been going on for days now, but of course commercial airlines are not flying in and out of Kabul for obvious reasons now.
"So we'll be coordinating with other EU countries primarily and also with the US to get our people out as quickly as we can."
Coveney also said Ireland had agreed to waive visas for 45 citizens escaping Afghanistan, some of whom were already in Pakistan.
As well as this, Coveney said Ireland had agreed to take in 100 to 150 refugees with a focus on "the vulnerable" including women and girls, media workers and human rights workers.
He added that this is a very small number and Ireland would likely have to do more.
Footage taken at Kabul airport shows harrowing scenes of thousands of Afghans attempting to flee the country to escape the Taliban rule.
