Two men armed with handguns approached the ticket office at around 5 pm, while a few visitors were still queueing to enter, Rai News reported.
One of the robbers aimed his gun at a member of staff while the other forced another employee to lead him to the museum's safe. The thieves dragged the safe to the exit, where a third accomplice was waiting in a get-away car.
No one was reported injured.
Police are using witnesses' account and CCTV footage to try to identify the men, whose faces were covered for the heist.
The Centrale Montermartini was closed on Monday as usual. Housed inside a former power station in the industrial-turned-trendy neighbourhood of Ostiense, the public museum displays ancient sculpture and artefacts that belong to the municipality of Rome.
Nothing was stolen from its collection in Sunday's robbery.
More daring art heists in Italy have seen thieves make off with works worth millions of euros. In 2015, a gang stole masterpieces by Rubens and Tintoretto from a museum in Verona with the help of a security guard, while several precious paintings have been snatched from churches.
And in January, jewels worth several thousands of euros and owned by Qatar's ruling family were stolen from a show at the Doge's Palace in Venice.