The moon began to move between the Earth and sun at 6:19 am (2319 GMT Tuesday), and about an hour later a total eclipse became visible in western parts of the country.
The sun then went entirely dark in a broad arc right across the country, to the eastern Maluku Islands, before the eclipse swept out across the Pacific Ocean.
Partial eclipses were also visible over other parts of Asia and Australia, with schoolchildren in Kuala Lumpur donning special eclipse-viewing glasses to watch the spectacle and crowds gathering early in Singapore to witness the phenomenon.
"It was spectacular," said Daniel Orange, a 52-year-old American tourist from California, who was watching the total eclipse on the small western island of Belitung.
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"It was very beautiful, there are a lot of people here and when the totality hit, everybody cheered. I got goose bumps."
In the popular viewing spot of Ternate, in the Malukus, thousands of people watching the spectacle on a beach cheered loudly and yelled "Glory to God".
In Singapore a crowd of about 400 people, including students and families, gathered at a university sports field to watch the partial eclipse, while groups of enthusiasts also converged on beaches and outside their highrise apartments to gaze upwards.
Many came early with their cameras, long-range telescopes, and sunglasses.
For some of Indonesia's tribes, the eclipse is viewed with apprehension. In Palangkaraya, on Borneo island, Dayak tribesmen performed a special ritual to ensure that the sun, which they view as the source of life, did not disappear entirely.