The AKP, led by Prime Minister Recep Tayyip Erdoğan, says the 26 proposed amendments to the constitution will bring Turkey closer in line with standards demanded by the European Union, which the country is seeking to join.
But its opponents argue that the changes would allow the government excessive control over the judiciary, with parliament given more power to appoint judges.
Turkey's current constitution dates back to the early 1980s, when the country was under military rule following a coup.
The reforms would end the immunity from prosecution extended to the leaders of that coup. They would also make the military more accountable to civilian courts.
In addition, the package gives civil servants the right to collective bargaining, and increases women's and children's rights.
The EU has welcomed the proposed amendments as "a step in the right direction", though it expressed reservation about increasing the government's influence over the judiciary.
The predominantly Islamic AKP has clashed repeatedly with courts over the protection of Turkey's secular values. The Constitutional Court came close to banning the party in 2008 for undermining secularism.
Even if the revisions are passed in Sunday's vote, Turkey's constitution will still fall short of EU standards, says RFI's correspondent in Ankara, Jasper Mortimer, particularly in terms of freedom of expression and making the armed forces more accountable to parliament.
"The prime minister has promised a much more major overhaul of the constitution if he's re-elected in next year's general election," Mortimer says.
Polling stations close at 2 pm universal time, and results are expected several hours later.