The two small bombs, believed to be the work of Basque separatist group ETA, exploded on the Spanish island just over a week after ETA killed two police officers on the island.
No one was hurt in Sunday’s blasts and Spanish police defused a third device found nearby.
The Department of Foreign Affairs has decided not to issue any specific warning to Irish holidaymakers planning to travel to Majorca.
Around 136,000 Irish people holiday on the island each summer. On its website, the department advises tourists to “take normal precautions” and to stay alert.
“Irish citizens should be vigilant and be aware that attacks could be indiscriminate and include places frequented by foreign tourists.
“At all times you should follow the instructions and advice of the local police and your tour operator,” the department website says.
It says the department is confident the Spanish government and local security forces are fully alert to the threat of terrorism and are taking substantial measures to counter this threat.
The Irish Travel Agents Association also dismissed fears that Irish holidaymakers travelling to Majorca face renewed threats to their lives and wellbeing.
“Obviously, there are concerns, but most people on holiday there would not even be aware of what it is happening. It tends to be the grannies at home rather than those in Majorca who are most worried,” said Simon Nugent, chief executive of the association.
“Majorca has always been a very popular destination for Irish holidaymakers and this is not going to change because of recent events there,” Mr Nugent added.
“In any event, these latest attacks seem to be an attempt to target the symbols of the Spanish state rather than tourists and are designed to cause anxiety more than physical hurt to people.”
Hours ahead of Sunday’s attacks, two Basque men wanted in Spain in connection with ETA terrorism addressed an audience in Belfast.
Ianaki Juana de Chaos and Arturo Benat Villanueva are fighting extradition from the North. Chaos, who was involved in a 1980s bombing campaign which killed 25 people, will appear again in a Belfast court next month.
The two Basques appeared as part of the west Belfast festival, Féile an Phobail at what was billed as a “political persecution” discussion.
The pair have received support from Sinn Féin MEP Bairbre de Brún and Breandán MacCionnaith of the splinter republican group Éirigí.