The museum said it recognised the issue, but concerns regarding the building maintenance meant it could not allocate sufficient funds for accessibility improvements at this time.
The exhibition, "The Kingdom", is on at the museum’s Animal Attic and is only accessible by stairs.
Dunedin disability advocate Amy Taylor said the exhibition drew the interest of the disabled community and not being able to view it was upsetting for some.
"It just makes us feel like we have a really low priority.
"There’s no excuse for the area of the animal attic not being accessible," Dr Taylor said.
She questioned why a ramp could not be installed to allow access.
"It’s only a few steps, but a few steps if you’re a wheelchair user is a barrier.
"The [exhibit] items are also pretty small, so you can’t view them from afar.
"You can’t stand at the bottom of the stairs to view them."
The facility was publicly funded, so she did not see finances as an excuse.
There were no audio descriptions of the pieces in the exhibition, so members of all sides of the disabled community were affected, she said.
"If you’re deaf, there’s no sign language.
"There’s a touchscreen, but if you’re blind, what use is a touchscreen?"
Otago Museum director Ian Griffin said financial constraints prevented the museum from creating an online version of the exhibition or providing alternative formats, such as audio descriptions.
"We acknowledge the impact this has had and are committed to learning from this experience."
Marketing manager Charlie Buchan said the museum recognised accessibility could be an issue.
"We have taken steps to improve it where possible, such as installing full screens at the bottom of the stairs to display all items."
The museum was also looking into improvements to the shop counter and continued accessibility was a priority in long-term planning, Mr Buchan said.