The Script guitarist Mark Sheehan playing the Big Weekend event in Derry in 2013
The 46-year-old died in hospital on Friday following a brief illness, the band announced.
Sheehan formed the group in 2001 alongside vocalist Danny O’Donoghue and drummer Glen Power.
A statement on the band’s social media pages said Sheehan was a “much loved husband, father, brother, band mate and friend”.
It asked fans to respect the privacy of his family and bandmates.
Ireland’s president Michael D Higgins said Sheehan was an “outstanding” example of Irish musical success on the world stage.
“It was a mark of the originality and excellence that Mark and his bandmates in The Script sought that they saw such success across the world, including six number one albums in the UK and a number three album in the United States – a truly remarkable achievement,” he said.
The Script played Radio 1’s Big Weekend event in Derry in 2013.
Contemporaries of Sheehan’s in the entertainment industry were quick to honour his memory.
In a statement posted on Instagram, Irish presenter Laura Whitmore wrote: “Thinking of you all at this time.
“Mark was one of the nicest and most talented men you could meet.”
Fellow Irish rock band Kodaline have also paid tribute, posting on Twitter: “So sorry to hear (of) the passing of Mark Sheehan.”
The Script are scheduled to support the American artist Pink during her European tour later this year.
