Lord Browne, a member of the Assembly’s culture, arts and leisure committee, questioned the use of the library for what he described as “a highly sensitive” exhibition.
Deputy First Minister Martin McGuinness officially opened the exhibition on the hunger strike which he described as “one of the most seminal events in the history of the Troubles”.
Mr McGuinness said the display is a “very powerful” exhibition which was being held in a “very respectful and dignified” way, and he acknowledged that republicans were “not the only ones who have suffered”.
He was joined by Sinn Fein colleagues from the Assembly and newly-elected TDs Gerry Adams, for Louth, and Mary Lou McDonald, for Dublin Central.
The extensive exhibition includes artefacts and items of clothing worn by some of the 10 republicans who died at the Maze prison during the protest against the British authorities who denied the prisoners political status.
However, Lord Browne said the hunger strike remains a very sensitive issue.
“An exhibition like this could prove offensive to people from the unionist community and one should be careful, as it is a public place,” he said.
“It is up to the trustees of the Linen Hall Library, but I think they should take people’s sensitivities into consideration.”
Linen Hall Library director Brian Adgey said the exhibition was a private launch by Sinn Fein.
“We are a neutral venue dedicated to providing collections and information to the people of Ireland, primarily Northern Ireland. The Linen Hall library puts on its own exhibitions for the public to make up their own minds, but this is Sinn Fein’s own exhibition,” he said.
The hunger strike exhibition will tour Ireland throughout the 30th anniversary year.
It will move from Belfast to Dublin, then on to Ballymena and Omagh.
The hunger strikes were a pivotal moment in the history of the Troubles, which led to republicans moving into the electoral process. Bobby Sands, a prisoner at the Maze, refused food on March 1, 1981. He was joined by other prisoners who were protesting in order to be given political prisoner status instead of being treated as criminals. Sands died after 66 days — he was one of 10 republicans who died. While on hunger strike, Sands stood for and won a seat at Westminster.