The package put to the country's 6.3 million voters is being boycotted by the opposition and has left much of the electorate confused, analysts say.
Commentators say turnout for the referendum is the main question, as there seems to be little doubt the changes will be approved.
Two opposition coalitions claimed turnout was very low, estimating that only between three and seven per cent of eligible voters had cast a ballot. Official figures have yet to be released.
Ouattara must now either withdraw the text or resign, he added.
Voting ended at 1800 GMT. An electoral commission source previously said the counting should be finished "by the end of Monday, Tuesday at the latest".
President Alassane Ouattara's revised constitution would create the post of a vice president, and set up a senate, a third of which would be nominated by the head of state.
The issue of identity has contributed to years of unrest in the West African country, which suffered a coup in 1999, a civil war in 2002 that split the country between its north and south, and a bloody post-election crisis in 2010.
The electoral crisis led to months of post-poll bloodshed with then-president Laurent Gbagbo refusing to step down.
Shortly after the polls opened at 0800 GMT, trouble broke out in the economic capital Abidjan and elsewhere, with groups of youths storming several voting stations and damaging equipment, Interior Minister Hamed Bakayoko said.
Bakayoko described incidents at "around 100" of the country's 20,000 polling stations.
"They started by throwing stones... Then they came in and broke everything.... They told us to stop working 'because the constitution doesn't meet the people's expectations'," an official, Nandy Bamba, told AFP.
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