In a post on X, formerly Twitter, Mr Zelenskiy said he held an “unscheduled meeting” with Gen Abdel Fattah al-Burhan at the airport.
Gen Burhan, president of Sudan’s military government and head of the army, has been on one side of a violent conflict in the north African country, which broke out in April this year.
Mr Zelenskiy said the meeting in Shannon Airport discussed the activities of Moscow-funded armed groups.
Russia’s Wagner mercenary group has operated in Ukraine throughout the country’s invasion. Western diplomats and media have said the group is also present in Sudan, although Wagner denied this.
In his post on X, Mr Zelenskiy said he was grateful for Sudan’s “consistent support of Ukraine’s sovereignty and territorial integrity”.
“We discussed common security challenges, namely the activities of illegal armed groups financed by Russia,” he said.
“I invited him to support the Grain From Ukraine initiative and take part in this year’s summit. We considered possible platforms for intensifying co-operation between Ukraine and African countries,” he said.
On Friday, the Ukrainian president had been on a visit to Canada, where he addressed the country’s parliament, and before that had been in Washington.
A spokesman for the Department of Foreign Affairs said the meeting between Mr Zelenskiy and Gen Burhan took place during a “technical stopover” at the airport.
“As per normal practice for stopovers at this level, protocol staff of the department were on the ground to offer practical assistance,” he said.
In a formal address to the UN in New York on Friday, Taoiseach Leo Vararkar condemned the war in Ukraine as an “imperialist and brutal invasion” and also hit out at Russia for ending the Black Sea grain export deal and over threats to use nuclear weapons.
Mr Zelenskiy last year made an address to a joint sitting of the Houses of the Oireachtas. He said that while Ireland is a neutral country, it has “not remained neutral to the disaster and to the mishaps that Russia has brought to Ukraine”. Speaking via video link, Mr Zelenskiy thanked Ireland for the humanitarian and financial support it has provided to his country.
Gen Burhan - who seized power in a coup in 2021 - addressed the UN General Assembly in New York this week and is on a global diplomatic tour seeking international support and some kind of legitimacy for his leadership, despite his failure to hand power to civilian authorities.