Trevor O'Neill was shot outside a supermarket in Majorca just after 21:00 local time on Wednesday, Irish national broadcaster RTÃ‰ reports.
His shooting is understood to be linked to a feud between Irish criminal gangs.
Mr O'Neill's partner and three children, aged five, seven and 10, were with him when the attack happened.
They had travelled to Majorca on Saturday for a holiday for his 40th birthday.
Police believe the attack was connected to a dispute between the Hutch and Kinahan groups, but Mr O'Neill was not the intended victim.
The feud between the gangs was sparked by the killing of Dubliner Gary Hutch in Spain last year and most of the resulting violence and murders have happened in Dublin.
Attempts to revive Mr O'Neill at the scene failed and police are said to be searching for up to three suspects.
It is understood that he was not linked to organised crime but may have been talking to a member of the Hutch family at the time.

The incident happened after the vehicle left the A68 in Jedburgh at about 09:40.
Police said a "small number of passengers" on board had been left shaken and were checked over by paramedics at the scene.
Investigations are continuing to determine what caused the bus to leave the road.
It hit a car and also struck a roadside wall a number of times before travelling across a grassy area and finally coming to rest against a metal barrier overhanging the Jed Water.
The route was closed for about an hour while the vehicle was safely removed from the scene.

The 56-year-old man, from Essex, was pronounced dead at the scene of the crash in a field off Burrows Lane, in the Middle Stoke area, on Sunday.
His next of kin have been informed. No-one else was in the aircraft.
The Air Accidents Investigation Branch (AAIB) attended and are investigating the cause of the crash, which happened at about 16:18 GMT.
Louise Holloway, who lives nearby, was outside in the garden when she heard a "huge bang" and saw "a massive orange flash right across the sky".
"One man ran across the field but there was no way the pilot could have got out. It's really sad," she said.
Representatives from UK Power Networks and fire crews also attended.
An Irishman who was shot dead on a Spanish island is believed to have been killed in a case of mistaken identity in a gang-related attack.
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