Adrian Ismay, 52, was the only person wounded in the March 4 attack in Belfast, the capital.
"Adrian Ismay gave over 28 years of service to prisons in Northern Ireland and he was greatly respected by all those who knew him," Justice Minister David Ford and Northern Ireland Prison Service Director General Sue McAllister said in a joint statement.
"Our thoughts and prayers are with his family, friends and colleagues at this difficult time."
It was not immediately what exactly caused Ismay's death. The Police Service of Northern Ireland earlier indicated that he suffered severe but not life-threatening injures.
On Saturday, suspect Christopher Alphonsos Robinson appeared in a Northern Ireland court to face charges
related to the bombing: attempted murder of a prison officer and having explosives with intent to endanger lives, according to court officials.
When a court clerk asked him if he understood the charges, Robinson did not reply but instead gave a loud sigh, officials said.
His lawyer told the court that in 16 police interviews, Robinson was not shown any evidence linking him to the attack. But a detective said, also in court, that police can link the 45-year-old from Dunmurry, on Belfast's outskirts, to the crime.
'Extremely high' threat of dissident attacks
The bombing raised alarms, and not just because of the violence of this particular act. Many fear it could be a sign of more carnage to come ahead of a dissident uprising's milestone anniversary.
That revolt, known as the Easter Rising, happened in 1916 in Ireland.
A small force of nationalists managed to briefly occupy parts of Dublin before being defeated by the then-controlling British forces. Yet the dissidents kept on fighting, ultimately helping to secure Ireland's independence a few years later.
Northern Ireland still falls under the UK umbrella, though it has seen plenty of tension and violence.
Nearly 3,600 people died in a late 20th-century conflict known as "The Troubles," that pitted pro-British Protestants against Catholics who wanted to wrest Northern Ireland from British control and unify it with Ireland.
That violence largely ended with the historic Good Friday power-sharing agreement in 1998. Still, the opposition to British rule never went away entirely.
Following the March 4 Belfast bombing, Northern Ireland Assistant Chief Constable Stephen Martin said there was an "extremely high" threat of more dissident attacks in conjunction with the Easter Rising centenary. At least four events are being held to mark the uprising, the first on March 26.
Security forces have beefed up their presence in key locales, concerned that splinter groups from what was once the Irish Republican Army will target police, prison officers and soldiers, according to Martin.