Two masked men smashed display cabinets and took more than 60 objects after overpowering a guard at the museum in Olympia, officials said.
The town's mayor said the items, mostly bronze and clay statuettes, were of "incalculable" value.
Culture Minister Pavlos Geroulanos has tendered his resignation, but it has so far not been accepted.
He has gone to the site which is on a forested hilltop in western Greece.
The BBC's Mark Lowen in Athens says the robbery - the second major museum theft this year - raises fresh questions about museum security.
'Smashed windows
The armed thieves are reported to have entered the Museum of the History of the Olympic Games in Antiquity at 07:30 local time on Friday (05:30 GMT) and demanded that a female employee hand over various objects.
When the employee refused, she was tied up and gagged.
Olympia Mayor Thymios Kotzias said the robbers - one of whom had a gun - targeted the guard during a shift change, after having already knocked out the alarm.
"We must wait and see what the local archaeology supervisor will say, but the items were of incalculable value."
Pantelis Kapsis, a spokesman for the Ministry of State and Government, told the BBC some items had also been damaged in the raid.
"Because of the way they smashed the windows everything within the display windows was shaken. so some had shattered a bit, so we don't know exactly what was taken."
The town is home to two museums - the Archaeological Museum of Olympia, which contains some of Greece's most valuables treasures from the temples of Ancient Olympia - and the smaller Olympics museum, which is reported to be less well-guarded.
Hundreds of thousands visit Olympia - the birthplace of the ancient Olympic Games - every year.
Greece's culture ministry, like most state departments, has seen its budget cut as part of austerity measures imposed by the government.
In January, a Picasso painting, given by the artist himself, was stolen from the Athens National Gallery, along with a Mondrian painting and a sketch by Italian artist Guglielmo Caccia.
A unionist with the culture minister said museums nationwide are short of some 1,500 guards, after two years of layoffs imposed by the government, according to AFP.
"All museums have suffered cuts, both in guards and archaeologists, the staff are no longer enough to operate at full shifts," said Ioanna Frangou, general secretary of the union of short-term culture ministry staff.
.bbc.co.uk/
