The new 4,000-square-meter (43,000-square-feet) extension displays the remains of ancient baths and hot water pipes, public latrines, homes, wells and workshops, organizers said.
Most of the remains are Roman and Byzantine but "some date back to Classical Athens," said museum director Dimitris Pantermalis, phys.org reported.
According to Classical-era historian Thucydides, this particular part of Athens was first inhabited some 5,000 years ago, Pantermalis said.
The remains were first unearthed during the museum's construction between 1997 and 2004, but were previously only partially visible through the entrance glass floor.
Their excavation was delayed by the Greek economic crisis, organizers said.
Objects found during the dig are to be displayed at the museum at a later date.
Since it opened in June 2009, the Acropolis Museum has welcomed 14.5 million visitors.
The museum and the Acropolis are Greece's top two archaeological sites.
Designed by celebrated Franco-Swiss architect Bernard Tschumi, the three-level building offers panoramic views of the Acropolis citadel and showcases sculptures from the golden age of Athenian democracy.
Set out over a total area of over 14,000 square meters (150,000 square feet), it harnesses natural light to show off hundreds of artifacts and sculptures.
It includes a section reserved for the disputed Parthenon Marbles, currently at the British in London.
Greece has long pursued a campaign for the return of the priceless friezes, removed in 1806 by Lord Elgin when Greece was occupied by the Ottoman Empire, but the British refuses to repatriate them.