Police say an anonymous caller made the telephoned threat on Friday to a Greek newspaper, saying a bomb would explode at the landmark museum in 40 minutes.
The deadline expired without incident but bomb disposal experts are investigating the building, while authorities have diverted traffic and pedestrians away from surrounding streets.
The museum, just outside the ancient Acropolis site, is Greece's most popular, attracting about 1 million visitors every year.
It houses collections of sculptures from the citadel's marble temples, as well as free-standing statues and pottery excavated on the hill over the past century and a half.