The minister has set up a Culture Recovery Taskforce to recommend measures for entertainment venues to reopen and performances to resume.
Some plays, live music, performances and exhibitions resumed in England, Wales and Scotland on Monday.
Theatres in NI have been given an indicative date of 21 June to reopen.
But it is not yet clear if live music can return on that date.
Libraries, museums, galleries and cinemas are expected to open from Monday.
Arts, music, culture and heritage has been hit hard by the pandemic, with many venues closed to audiences since March 2020.
Indoor entertainment venues in England, Wales and Scotland reopened on Monday.
However, capacity is limited to 50%, or up to 1,000 people at most.
Social distancing and face masks are still needed but “Covid passports” or proof of a negative test are not required to enter a venue in England.
Ms Hargey said the 25-strong taskforce would consider how venues in the North of Ireland could open safely to audiences from June 21.
“We wanted to give that date so that it’s something to work towards,” she said.
“What I would like to see the task force do is how then we can open on 21 June safely.
“There are a number of pilots that are taking place in England, we’re obviously getting information on that via the SAGE committee which the health minister and the chief medical officer sit on.
“We’ll be monitoring those closely, and I want all of that to go through this taskforce.
“But also to look at the local knowledge and expertise here, people who run events, people who organise safety around key events in planning for coming into the summer season.
“But doing that in a safe way that keeps the opening long-term and sustainable.”
The taskforce includes those who run festivals, music, theatre and arts venues and organisations.
Ms Hargey said she also wanted to see live music resume “as quickly and as safely as possible”.
“I want to get venues a bit of normality back,” Ms Hargey said.
“We have obviously eased a good bit of restrictions around outdoor events and indoor events from next Monday.
“We want to build on that then to aim for 21 June to make sure that we can do that quickly and also as safely as possible.”
However, the minister also said that if some restrictions on performances or audiences remained there would need to be further financial support for venues and those working in the sector.
Ms Hargey said: “I would hope to go to some type of concert or outdoor venue, 100%.’
“I do hope through the taskforce and the work that we’ll be doing with the executive that we can see that ray of sunshine over the summer season, and particularly during festival season.”
The chairwoman of the taskforce, Rotha Johnston, said its purpose was both “recovery and re-opening in the short-term”.
“I think what the taskforce will want to look at are the measures that have been put in place for live performances across the water in England,” she said.
“What can we learn from those measures and can they be applied safely here?
“We will be guided by the views from the executive and the guidelines in place at that time, but the sorts of issues we’ll want to look at are in terms of capacity, in terms of social distancing, in terms of track and trace.
“But also for these organisations the viability – what does it mean for them opening in terms of those additional requirements.
“We’ll want to look at every possibility.”Tags: