The National Museum of American History is marking the 100th anniversary of one of its most popular exhibitions, “The First Ladies,” by displaying Michelle Obama’s second inaugural gown.

The floor-length, ruby-colored chiffon gown, designed by Jason Wu, is on loan from the White House for a year starting Tuesday and will be paired with Obama’s Jimmy Choo shoes in the exhibition center. Obama’s first inaugural gown, white with a long train, also designed by Wu, will not remain on display, but there will be a 2009 photo of the first lady wearing it....