The Monday vote is on proposals including raising the presidential term from five years to seven, granting the president the right to dissolve parliament and creating new appointed vice presidential posts.
Some opponents say the changes would strengthen what they see as effectively a dynastic system of rule in the oil-rich Caspian Sea nation, which comes under frequent criticism from abroad for alleged human rights abuse and suppression of dissent.
The Venice Commission, a European watchdog of constitutional law experts, last week said the measures would weaken political dissent.
Officials say referendum results will be announced by Oct. 21, according to the Associated Press.