The undersea quake had a depth of just 12.5 kilometres (7.7 miles) and struck northwest of the enclave's administrative capital of Karyes in the Halkidiki peninsula, the institute said on its website.
It was felt in surrounding areas and several aftershocks followed.
"We are well, people should not be worried," Mount Athos governor Alkiviadis Stefanis told state TV ERT.
One man visiting a monastery was taken to hospital with a hand injury after running and falling, he said.
There were no other reports of injury.
A fire department source in Athens told AFP that the area's four fire engines had been sent out in search of possible damage.
The tremor dislodged plaster and damaged chimneys at some monasteries, Stefanis said.
Grigoris Tasios, head of the Halkidiki hoteliers association, told ERT the tremor had not affected tourist infrastructure.
Seismologist Costas Papazachos told news portal NewsIT that the Halkidiki peninsula has seen a "steady" seismic activity in past months.
Mount Athos, an Orthodox spiritual centre since 1054, has enjoyed an autonomous statute since Byzantine times.
Known as the Holy Mountain in Greece, the community has around 20 inhabited monasteries, some of whom are over 1,000 years old.
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