“The allegations are of a grave nature. We are aware that these centred on issues of governance, nepotism and corruption,” Mthethwa said.
He said he had instituted an independent investigation into the management of the museum.
In November, a group of former political prisoners vowed to embark on a hunger strike if their demands were not met by the island’s management.
The Ex-Robben Island Political Prisoners Association of South Africa has slammed the management of the island for disregarding them.
The association submitted 18 questions in November to the management team.
These range from what steps had been taken to ensure that socio-economic benefits were available to former political prisoners - including those who work on the island, to what steps have been taken to improve relations with the workers.
They are also demanded answers as to what steps Robben Island Museum had taken against those found guilty of price fixing and collusion by the Competition Commission.
Mpho Masemola, the national secretary of the association, said: “We welcome the minister’s response to these grievances, however we would like the minister to act urgently and dissolve the board and suspend the chief executive, and then they will be able to start their investigation because they (the board and chief executive) can influence and cover their tracks.”
Masemola said that the association still intended occupying the island and that they would be embarking on their hunger strike.
“We cannot allow our island to be run by criminals - not in the name of Mandela - we will not be silent about it, we will defend our heritage,” he said.
The island has been in the news for all the wrong reasons, with ferries needing urgent repairs and being drydocked for months on end.
The museum has, in the meantime, asked for tenders to produce four DVDs on the lives of former political prisoners.
This while some of its ferries have not been operational and millions have been spent on maintenance.
Workers at the museum said the ferry Sikhululekile, which has been in for repair for months, is having an impact on their job security.
In March, staff downed tools to hand in a list of grievances to the management of the World Heritage Site.
Sibusiso Buthelezi, the chairperson of the council at the museum, said: “We welcome the investigation because we believe it will bring this madness to an end. I don’t think its right to say we should get rid of the chief executive when the chief executive has done everything in his power to maintain the island and he has done an excellent job.”