The outcome will also shape Turkey's strained relations with the European Union. The NATO member state has curbed the flow of migrants — mainly refugees from wars in Syria and Iraq — into the bloc but Erdogan says he may review the deal after the vote.
Some 55 million people are eligible to vote at 167,140 polling stations across the nation which opened at 7 a.m. (0400 GMT) in the east of the country. Voting in the rest of the country begins at 8 a.m. and closes at 5 p.m. (1400 GMT). Turkish voters abroad have already cast their ballots.
Ahead of the start of voting, Kurdish militants killed a guard in an attack on a vehicle carrying a district official from the ruling AK Party in southeast Turkey on Saturday night, security sources said.
They said the Kurdistan Workers Party (PKK) militants carried out the attack in the Muradiye district of the southeast's Van province. A second of the AKP official's guards was wounded in the attack.
The referendum has bitterly divided the nation. Erdogan and his supporters say the changes are needed to amend the current constitution, written by generals following a 1980 military coup, confront the security and political challenges Turkey faces, and avoid the fragile coalition governments of the past.
Opponents say it is a step towards greater authoritarianism in a country where around 40,000 people have been arrested and 120,000 sacked or suspended from their jobs in a crackdown
following a failed coup last July, drawing criticism from Turkey's Western allies and rights groups.
Relations between Turkey and Europe hit a low during the referendum campaign when EU countries, including Germany and the Netherlands, barred Turkish ministers from holding rallies in support of the changes. Erdogan called the moves "Nazi acts" and said Turkey could reconsider ties with the European Union after many years of seeking EU membership.