The Department of Foreign Affairs said it is providing consular assistance to the family of the woman, thought to be aged 50.
The extreme Somali group al-Shabab carried out the attacks that left at least 74 dead at a rugby club and restaurant in the capital Kampala.
They came two days after one of the group’s leaders called for attacks in Uganda and Burundi, two nations that contribute troops to the African Union peacekeeping force in Somalia.
The choice of two soft targets filled with civilians also raised concerns about the capabilities and motives of al-Shabab.
Foreign Affairs Minister Micheál Martin who has just returned from a visit to the East African country, said he was horrified and saddened by the loss of life.
“I know that the mood in Kampala yesterday would have been one of great joy, with celebrations to mark the conclusion of Africa’s first World Cup.
“The peace of those celebrations has been cruelly shattered by this heinous terrorist attack which I utterly condemn.
“On behalf of the Government and people of Ireland, I send heartfelt sympathy to the government and people of Uganda, especially to the bereaved and I offer my best wishes for a swift recovery to the injured.”
The minister said the Irish embassy in Kampala was offering consular assistance to the relatives and friends of those who may have concerns about the welfare of Irish citizens in Uganda.
Al-Shababin Mogadishu said it was responsible for the bombings.
A Ugandan government spokesman said it appeared two suicide bombers took part in the attacks, which left dozens wounded.
The attacks appeared to represent a dangerous step forward by al-Shabab, analysts said, and could mean that other countries working to help Somalia’s government will face attacks.
“Al-Shabab has used suicide bombers in the past and shown no concern about civilian casualties in its attacks,” said David Shinn, a former US ambassador to Ethiopia. “Some elements of al-Shabab have also prohibited the showing of television, including the World Cup, in Somalia.”
Ugandan president Yoweri Museveni vowed: “We shall go for them wherever they are coming from. We will look for them and get them as we always do.”
Al-Shabab, which wants to overthrow Somalia’s weak, UN-backed government is known to have links with al-Qaida. It also counts militant veterans from the Iraq, Afghanistan and Pakistan conflicts among its ranks as well as young men recruited from the Somali communities in the US.