The south Belfast attraction reopened on Thursday, along with Hillsborough Castle and Gardens in Co Down.
Safety measures are in place to facilitate social distancing.
The first visitor through the doors at the Ulster Museum was student Anna Lakse from Dublin.
“It was kind of an accident, I hadn’t been to Belfast before and I kind of stumbled across the museum,” she told the PA news agency.
“It is a very good system in the museum, I was happy with the way it was so spaced out and people were not on top of each other, you feel very comfortable.
“It’s nice to be able to get out now and not be stuck in the house. I’m really happy I came up to Belfast.”
Kathryn Thomson, chief executive of National Museums Northern Ireland (NMNI), said it was a fantastic day.
“The Ulster Museum is the first of our four museums to open, we are absolutely thrilled,” she said.
“We believe we have worked really hard to make sure that we follow all the government guidance.
“We have appropriate social distancing and really good hygiene in place throughout the museum and we are really confident that we are welcoming visitors in to a safe and very welcoming and warm environment.”.
Visitors must pre-book visits via the Ulster Museum’s website, as well as filling in a safety form and observing social distancing rules.
Of the other attractions run by NMNI, the Ulster Folk Museum in Cultra and the Ulster American Folk Park in Omagh will reopen on August 13, while the Ulster Transport Museum will follow on August 20.
Ms Thomson said it has been a difficult time in the culture, arts and heritage sector.
“We are a sector that has been encouraged over a number of years to build our own self-generating income and become less reliant on government funding so to lose all of that provides a very very challenging situation,” she said.
“It is challenging for everyone across the sector and we have had to work really hard to try and see what we can avail of from government support.
“We are confident that we can at least get ourselves through this year but we need our visitors to come back.”
Hillsborough Castle and Gardens in Co Down also reopened on Thursday, while Titanic Belfast will reopen on Saturday.


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