Barber believes the purpose-built stadium is “important” to give “respect and focus” to the women’s team.
He hopes this will help the club build a fan base and capitalize on the growth of women's football in England.
“I think every club in the country is looking at how they can integrate women's and girls' football more into their core operations,” Barber added.
“Some clubs have different strategies for us but we feel a women's stadium would be great for the city.
“We believe this will help us build an audience for the women’s team which we don’t currently have and we see this as a long-term project.
“Women’s football is growing rapidly and we see it as a very viable proposition for the future.”
Brighton's plans for the stadium include a “slightly modular” approach that will allow them to expand its size as the crowd grows.
But Barber admitted it was “not out of the question” that the men's and women's first teams could play regularly at American Express Stadium in the future.
He added: “I don't want to put out numbers at the moment because that would be a bit premature when we are still talking to stakeholders and local authorities.”
“Eventually, at some point in the future, it is not unlikely that we will unite our men's and women's teams again at the Amex – when we can perhaps modify some of the facilities we have to suit the women's team.
“But in the short to medium term, I think building a dedicated women’s stadium is the right way for us to grow our program.”