The moon began to move between the Earth and sun at 6:19 a.m (0449 IST today), the official Meteorology, Climate and Geophysics Agency said.
A rare total solar eclipse will be visible in a broad arc across the country about an hour later.
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From a festival featuring live bands, to fun runs and traditional dances, events are being organised across the country for an estimated 10,000 foreign visitors and 100,000 domestic tourists who will be witnessing the phenomenon.
Hotels in the best viewing spots filled up weeks ago -- in the city of Ternate, in the Maluku Islands, officials have had to find extra space for tourists on boats.
"It's an extraordinary spectacle that only takes place about once a year in one part of the world," said Arnaud Fischer, a 33-year-old French tourist, who has witnessed several eclipses and was set to watch today's in Ternate.
I Gde Pitana, the government's head of foreign tourism, described the phenomenon as "a tourism attraction created by God".
However there are concerns that clouds could obscure the view in some places, as it is currently the wet season in Indonesia.
It will be a deeply spiritual experience for many in the world's most populous Muslim-majority country, with the faithful being urged by Islamic authorities to perform special eclipse prayers.
"Our Prophet Mohammed said the prayer signifies the greatness of Allah, who created this wonderful phenomenon," said Ma'ruf Amin, chairman of the Indonesian Ulema Council, the country's top Islamic clerical body.
Some of Indonesia's tribes people are fearful of the phenomenon, however. Members of the Dayak tribe in one part of Borneo island will perform a ritual to ensure that the sun, which they view as the source of life, does not disappear entirely.
The total eclipse will sweep across 12 out of 34 provinces in Indonesia, which stretches about 3,000 miles (5,000 kilometres) from east to west, before heading across the Pacific Ocean.
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