Mr Obama said he hoped that the Sewall-Belmont House, once the home of the National Woman's Party, would become a symbol of women's rights.
In 1916, Suffragist Alice Paul founded the National Woman's Party, which fought for social and economic quality.
The museum is in downtown Washington, not far from the US Capitol building.
"I want young girls and boys to come here, 10, 20, 100 years from now, to know that women fought for equality, it was not just given to them," Mr Obama said.
The dedication on Tuesday was one of number of events marking Equal Pay Day. The day is designed to draw attention to the disparity in wages between men and women in the US.
In the US, the median annual pay for a woman who holds a full time job is $39,621 (Â£27,775) while the median annual pay for a man who holds a full time job is $50,383.
That $10,762 gap translates to US women earning just 79% of what their male counterparts make.
President Barack Obama has dedicated a new national monument to women's equality as he and others pushed for equal pay for women.