It asked them to support or reject a change to the 78-year-old document which reads: "Marriage may be contracted in accordance with law by two persons without distinction as to their sex."
Equality: Senator David Norris is welcomed by Andrew Hyland of YES Equality (left) as he arrives at a count in Dublin
Brian Lawless/PA
It does not suggest any change to the definition of the family or remove any outdated references in the section, including those that state a woman's place is at home.
If passed, it would be the 34th amendment to the constitution but, regardless of the result, the campaign will rank with other hotly-contested issues such as divorce and abortion.
Other countries have held referendums on gay marriage, including Croatia, Slovakia and Slovenia, where the extension of the right was not passed by the electorate.
In a separate referendum also being held today, voters are being asked their views on proposals to reduce the age limit on who can stand for the presidency from 35 to 21.