Deirdre Hargey said she is looking at an indicative date of June 21.
That date needs to be approved during a review of Covid-19 restrictions by Stormont ministers next week.
The Executive meets next Thursday, June 10 to discuss the lifting of the last of the lockdown restrictions.
Ms Hargey also said she hoped the 500-person cap on outdoor gatherings can be removed and replaced with risk assessments.
No live music is permitted in pubs and clubs under current Covid-19 regulations.
Arts, music, culture and heritage has been hit hard by the pandemic, with many venues closed to audiences since March 2020.
Risk assessments are being used to determine capacity for venues hosting weddings, funerals and outdoor gatherings for fewer than 500 people but more than 30.
Ms Hargey said that the indicative 21 June date is “predicated on the health advice, so I’m working that we can have live music back in venues as soon as possible”.
She added that indoor events would “maintain a level of social distancing” but that she was “hopeful that we can look at the cap as part of this for outdoor gatherings”.
“I am looking as part of this package of relaxations, if the health advice allows it, that we can lift that cap as well.”
Promoters of outdoor music festivals say the cap on outdoor gatherings has to be revised so outdoor music events can be economically viable.
They say if there are any social distancing measures in place, it won’t “add up”.
One figure being suggested is allowing only 500 people for an outdoor concert but promoters believe this would need to be increased to make the event financially viable.
Some plays, live music, performances and exhibitions resumed in England, Wales and Scotland May 17.Tags: