The reform, backed by the Council of Europe, would curtail the powers of the president and increase those of parliament.
On Sunday, polling stations opened at 8am (0400 GMT) across Armenia.
Armenia's 2.3 million registered voters are to approve or reject a text that would decrease presidential powers and increase those of parliament and the government, strengthen judicial independence and allow millions of diaspora Armenians to obtain citizenship by scrapping a ban on dual citizenship.
The reforms were drafted with the assistance of the Council of Europe, of which Armenia is a member, and the body called on voters to approve them.
Rene van der Linden, the head of the council's parliamentary assembly, said recently: "This is an occasion for Armenians to show their commitment to Europe."
The reforms are part of Armenia's commitments before the council, which could take disciplinary measures against Armenia if the vote fails as it did two years ago when the referendum was scrapped because of a low turnout.
To be adopted, the reform needs more than a third of the registered voters to cast ballots, and a majority of those voting in favour.
But the opposition, which unites 18 political parties and non-governmental organisations, has called on voters to boycott the referendum, saying the vote will legitimise the government of President Robert Kocharian.
Kocharian first came to power in 1998 and was re-elected in 2003 in a vote that many observers said was marred by fraud.
The opposition was to hold a rally late on Sunday, an hour before the polling stations closed.