Correa is locked in a battle with President Lenin Moreno for control of their deeply divided leftist ruling Country Alliance party.
The referendum, in which Moreno backs the "yes" vote, featured seven questions including reintroducing term limits to prevent presidents from running indefinitely.
If the current head of state gets his way, Correa will not be able to join the 2021 election race.
The National Electoral Council said the ballot "took place normally" with no significant incidents to report. It was expected to give preliminary results around 8:00 pm.
Moreno, as he voted in the north of the capital Quito, said the result would be "transcendental for the future of the country, so that our children are protected, so that corrupt people do not return to mock us... for the care of the environment, for economic reactivation.
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